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Home Posts tagged "Drake"
Tag: Drake
Kanye West Claims Drake Is Threatening Him In Escalating Beef
By Ambresia Reid December 15, 2018	 December 15, 2018 christmas, Drake, ep, Kanye West, la, lic, mo, nye, pop, rap, rap beef, Sicko Mode, travis scott, Twitter
The Kanye West vs. Drake beef has escalated severely over the previous 24 hours… The battle between the 2 A-List rappers runs deeper than in all probability any us can think about, however from what we will collect on Twitter it facilities round Travis Scott's "Sicko Mode." Kanye went one …
Apple Music Reveals Top 100 Most Streamed Tracks Of 2018
By Callie Mitchell December 6, 2018	 December 6, 2018 2018, apple music, Calvin Harris, Drake, Ed Sheeran, Grey, hea, hip hop, love, marshmello, Most Streamed, pop, rock, sad, summer, zedd
'Tis the season for high music lists. Every music supply has their concept high artists, albums, and songs for the 12 months — however Apple Music is a superb indicator the music that finest represents 2018. According to the favored streaming service (and it's arduous to argue) Drake is popping …
Spotify Reveals The Most Successful Artists, Albums & Songs of 2018 By The Numbers
By Talal Tuma December 5, 2018	 December 5, 2018 2017, 2018, Ariana Grande, Cardi B, Drake, Ed Sheeran, hea, hip hop, No, pop, post malone, rock, sad, Spotify, XXXTENTACION, year in music
Another 12 months, one other Spotify end–year listicle for essentially the most trafficked streaming platform on the earth. Spotify's annual Year In Music 2018 exhibits a a lot totally different panorama than what , however one that might have been simply predicted. Hip hop reigns supreme as Drake ousts Ed …
BREAKING: Travis Scott Releases Highly Anticipated Skrillex Remix of "Sicko Mode"
By Talal Tuma November 28, 2018	 November 28, 2018 astroworld, bass, Drake, lic, Mix, mo, Music, No, remix, Sicko Mode, Skrillex, travis scott
We could have to attend till Friday for the ficial "launch" Skrillex's remix Travis Scott's "Sicko Mode," a minimum of so far as streaming providers are involved, however you possibly can nonetheless get it now if you would like. The remix simply appeared on Travis Scott's on-line retailer . After …
Spotify Reveals All-Time Top Streamed Artists, Songs & Albums for 10-Year Anniversary
By Morgan Jamieson October 12, 2018	 October 12, 2018 Calvin Harris, Coldplay, dance, Drake, Ed Sheeran, edm, Eminem, justin bieber, Kanye West, love, Most Streamed, music streaming, No, rihanna, rock, Spotify, the chainsmokers
Spotify has been round for a decade — and in that point the streaming service has seen many chart-topping acts. Some set themselves aside from the pack, racking up thousands and thousands, even billions performs. To mark 10 years, Spotify is sharing its record prime artists, songs, and albums. EDM's …
Drake Postpones Two Shows Due To Serious Illness, Required "Round The Clock Care"
By Danny Murphy September 24, 2018	 September 24, 2018 cancelled show, concert, cover, Drake, ep, hospital, illness, miami, missed show, mo, No, personal, rap
Drake unexpectedly postponed two Miami reveals this week and now it's been discovered it was on account of sickness. With brief discover, the king's Friday and Saturday evening live shows at American Airlines Arena had been put f on account of what the venue described as "circumstances out our management." It was rumored …
Marshmello, Zedd & The Chainsmokers Battle It Out In The AMA Nominations
By Brad Walker September 13, 2018	 September 13, 2018 american music awards, Cardi B, dance, Drake, electronic, hea, hip hop, Nominations, pop, Queen, rap, rock
The 2018 American Music Awards nominations are in! Leading the pack we have the reigning king and queen hip hop, Drake and Cardi B. Each have a total eight nominations, or eight potential wins if one or the other is able to sweep the awards show. Ed Sheeran and Post …
Spotify Responds After Nicki Minaj Puts Streaming Service On Blast
By Amy Slaton August 21, 2018	 August 21, 2018 beef, billboard, Drake, ep, la, mo, Music, music streaming, Nicki Minaj, No, Queen, Spotify, travis scott, Twitter
Nicki Minaj isn't too pleased with Spotify right now. Particularly as it concerns her new album and, in her opinion, the streaming service's lackluster promotion surrounding the release. Referencing Drake's recent Scorpion SZN , which left many subscribers outraged, Minaj went f on Twitter… "Spotify had to teach me a lesson but …
Here's The First Artist In The World To Achieve Over 50 Billion Music Streams
By Talal Tuma August 11, 2018	 August 11, 2018 50 billion, dance, death, Drake, hold, label, Music, News, No, sad, scorpion, Spotify, Streaming
A news release from Republic Records Media confirmed the 50 billion total streaming milestone, according to . The achievement comes after the success Drake's album Scorpion, which was also the first full-length record to rack up one billion streams in a week, reported. Drake also destroyed Spotify and Apple Music's …
Is The #InMyFeelings Challenge Worth Jail Time?
By Brad Walker July 31, 2018	 July 31, 2018 dance, Drake, ep, fines, In My Feelings, internet, kiki, la, lic, Meme, Middle East, mo, News, No, outlawed, sensation, viral
You can't scroll through any social media platform without seeing a video someone dancing outside a car to the song "In My Feelings," by Drake. The viral challenge has taken the internet by storm but quickly turned dangerous. These videos seemed to be harmless but soon turned into its own meme …
Drake Has Made Over $100 Million On Spotify & Apple Music Alone
By Amy Slaton July 27, 2018	 July 27, 2018 ADE, ama, apple music, Drake, Ed Sheeran, ep, hea, kendrick lamar, mo, money, Music, Spotify, streams
While the competition between Apple Music and Spotify , Drake is headed to the bank. According to a new report from Music Business Worldwide, Drake has generated over $100 million across the two platforms from his music. Drake has been streamed over 10 billion times on Apple Music and over 13 …
Drake Shares Old Baby Photo Of Himself With His Dad
By Brad Walker July 26, 2018	 July 26, 2018 baby, baby photo, baby pics, Dennis Graham, Drake, Drake's Dad, instagram, Music, News, tbt
After sharing a low key weird photo him drinking a margarita on IG yesterday, decided to come through in the scary hours Thursday morning and share a few random photos on Instagram, one which was an old tbt pic him as a baby in his pops' arms. The however, was …
DeMar DeRozan Went To Drake's House After Learning Of Trade
By Brad Walker July 25, 2018	 July 25, 2018 demar derozan, Drake, nba, News, Sports, spurs, toronto raptors
DeMar DeRozan, now ficially a member the San Antonio Spurs, recently sat down with ESPN's Chris Hayne's for a in which the former Raptors All-Star spoke about the blockbuster trade and how the Raptors brass, including team president Masai Ujiri, assured him that he was not going to be traded. …
Drake's New Album Is The Lowest-Selling #1 Album Since 1991
By Brad Walker July 25, 2018	 July 25, 2018 2018, ADE, ama, Drake, low sales, mo, Music, music streaming, No, no. 1, post malone, sale, sales, scorpion
Music streaming is on the up, but album sales are devastatingly down. In fact, album sales in the U.S. are worse than they've been in over a decade — and streaming could be largely to blame. A current snapshot music sales comes with Drake's Scorpion. The album just set the bar …
Bella Hadid Calls The Weeknd Her "Muse Forever"
By Danny Murphy July 24, 2018	 July 24, 2018 bella hadid, couple, Drake, Entertainment, exes, friends, gossip, instagram, japan, Muse Forever, News, selena gomez, The Weeknd, tokyo
After hitting up a robot restaurant and karaoke bar , Bella Hadid and are still getting up to all kinds adventures in Japan. The former couple, who may very well be feeling things out again, hit up the Mori Building Digital Art Museum recently and Bella shared their experience with …
Shiggy Will Sadly Not Be In Drake's "In My Feelings" Video
By Danny Murphy July 24, 2018	 July 24, 2018 comedian, dance, dance challenge, Drake, In My Feelings, instagram, Music, News, ovo, questions, scorpion, Shiggy, video
One 's most popular Scorpion songs "In my Feelings" became famously more popular than anyone could have expected thanks to the man, Shiggy. The comedian shared a little dance to the beat and just like that it was turned into a dance challenge. Unfortunately, being as Shiggy did his two-step outside his …
"Rolling Papers 2" First Week Numbers Are In & Drake Remains #1 For Third Week
By Amy Slaton July 23, 2018	 July 23, 2018 ?, album sales, albums, Beerbongs And Bentleys, billboard, Cardi B, charts, Drake, first week sales, Goodbye & Good Riddance, hot 200, invasion of privacy, Juice WRLD, Music, music charts, News, post malone, Rolling Papers 2, scorpion, Streaming, wiz khalifa, XXXTENTACION
The music charts are being dominated by hip-hop artists right now. The top six albums in America all belong to rappers. 's Scorpion will spend its third week at number one on Billboard's Hot 200 chart. While that news is not shocking whatsoever, it does add another line to Drake's already astounding resume. …
Drake's "Scorpion" Reaches New Sales Low For The Week's Top Selling Album
By Talal Tuma July 21, 2018	 July 21, 2018 album sales, billboard, digital downloads, Drake, low, Music, News, nielsen music, physical pcopies, sales, Streaming
is prone to break records with whatever he releases. Whether its a single or an album, they usually go on to break streaming and Billboard records. Unfortunately, the rapper set a new record today but it might not be something he should be entirely happy about. Drake's sales for Scorpion on …
Drake Lost Out On Over $500,000 Dollars In Physical Sales Of "Scorpion": Report
By Brad Walker July 20, 2018	 July 20, 2018 $500,000, cd, cds, dollars, Drake, first week sales, lost, Music, News, physical copies, sales, scorpion
's wildly successful new album, Scorpion, has been available on streaming services since June 28, but that's not when the physical copies were released. In fact, the CD form the album wasn't released until two weeks later on July 13, a move that not only cost him at least $500,000 …
Drake Parties With 7 Gorgeous Women In Hollywood
By Danny Murphy July 19, 2018	 July 19, 2018 club, clubbing, clubs, Drake, girls, hollywood, ladies, los angeles, Music, News, parties, party, partying, tmz, video, women
is at a point in his life where he can get with any woman on the planet based solely on his celebrity status. While we've seen him out with plenty women in the past few weeks, they have all appeared to be solo dates. Perhaps the most eligible bachelor in the …
Is Drake Losing His Clout?
By Amy Slaton July 18, 2018	 July 18, 2018 #InMyFeelingsChallenge, clout, Drake, editorial, Features, In My Feelings, influence, Music, new generation, News, nonstop, scorpion, tay keith
Another album, another round streaming and chart records broken. On day one, Scorpion both Spotify and Apple Music's records for most album streams in a single day. In its first week out, it Post Malone's beerbongs & bentleys's first week streaming numbers, which were 2018's highest. It's also the to ever be …
Drake Name-Drop Delayed Jail Time For City Girls' Rapper J.T.: Report
By Danny Murphy July 18, 2018	 July 18, 2018 bet awards, City Girls, clout, court, delayed, Drake, florida, jail, jt, legal, miami, Music, name-drop, News, prison, sentence, Surrender
J.T. from City Girls has to thank for her newfound fame as well as her BET Awards appearance. The Miami rapper gained clout from her feature on Drake's "In My Feelings." This fact played an instrumental part in her jail check-in being pushed back. It is that J.T., whose real name …
J. Prince Says Drake's "Definitely Happy" That He Didn't Continue Pusha T Beef
By Morgan Jamieson June 26, 2018	 June 26, 2018 beef, diss track, Drake, Drake & Pusha T Beef, feud, j prince, Music, News, Pusha T, trl
The and beef may have ended but fans are still eager to here if the Toronto rapper addresses the feud on his upcoming album, Scorpion. There's no doubt that Push had the final word in the beef with his diss track, "The Story Of Adidon." While fans still wish they would be …
BlocBoy JB ft. Drake – Look Alive
By Amy Slaton February 9, 2018	 February 9, 2018 app, apple, Drake, la, live, Music, No, youtube
During Scary Hours, BlocBoy JB and Drake take it to Memphis for the catchiness "Look Alive." Stream the Tay Keith produced track on Apple Music right now.
Rhythm Roulette With @CardoGotWings
By Talal Tuma February 1, 2018	 February 1, 2018 Drake, ep, la, Migos, No, win, wiz khalifa, youtube
Its time to watch Cardo Got Wings at work. You may know him from his production credits on Meek's "Levels", Jeezy's "Seen It All" with Hov, his early work with Wiz Khalifa on Kush & OJ, "Deadz" with Migos and 2 Chainz, and his latest #1 record with Drake "God's …
Everyday Struggle With @IAmAkademiks & @Troitorain | 1.30.18 |
By Danny Murphy January 31, 2018	 January 31, 2018 2018, album, awards, Drake, grammy, grammy awards, la, youtube
The trio discusses the ratings drop the 2018 Grammy Awards, the return Drizzy Drake, Rae Sremmurd returning with three solo albums,
Did Drake Diss @JoeBudden On "Diplomatic Immunity?" Yes? No? Maybe So…..?
By Danny Murphy January 25, 2018	 January 25, 2018 dance, diplo, Drake, ep, hea, la, No, youtube
After taking over the TL with the release the Joe Budden Podcast yesterday, the boys dive deep into Drake's "Diplomatic Immunity" where Drake aimed a friendly bullet at Joe's head. In the video, Joe states that the line was nothing but factual while Rory and Mal are 100 percent sure …
@Diddy: "Me And 50 Cent Are NOT Cut From The Same Cloth…."
By Talal Tuma January 25, 2018	 January 25, 2018 club, Drake, gold, la, mo, writing, youtube
Diddy stopped by The Breakfast Club recently and spoke to the trio about his relationship with his children, his children's mother's, watching them grow up, being proposed to, dealing with 50 Cent's antics, his dealings with the Carolina Panthers, his top moments with Mary J. Blige and writing hits with …
REVOLT Unlocked With Cool & Dre
By Morgan Jamieson January 19, 2018	 January 19, 2018 chill, Drake, ep, la, love, miami, new york, youtube
REVOLT TV sits with Cool & Dre and gets some pretty epic stories behind some their biggest hits. And just in case you forgot what this Miami duo has produced, peep the credits below! Well some the credits lol. Ja Rule ft. Jadakiss & Fat Joe – New York Christina …


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Most Read: Contributor Ireland, October 2020
European Union: Ireland And The EU 2030 Climate Target Plan
by Alex McLean , Karen Killoran , Deborah Spence , Danielle Conaghan , Matthew Dunn , Nicole Ridge , Dearbhaile O'Brien and Katrina Donnelly
Arthur Cox
In 2019, the EU endorsed a new target of achieving net zero greenhouse gas emissions by 2050. However, it is predicted that current policies will only reduce emissions by 60% (as against 1990 levels) by 2050.
To begin to address the challenge ahead, the European Commission published the 2019 Communication on the European Green Deal ("EGD"), a growth strategy to reset the Commission's commitment to tackling climate change. It outlined an all-sector approach to reducing emissions and decoupling economic growth from resource use.
The Commission committed to presenting an impact assessed plan to increase the existing target for 2030 of reducing emissions by 40% to at least 50%, and towards 55% (as against 1990 levels).
Based on this impact assessment, the Commission published a Communication on Stepping up 2030 Europe's Climate Ambition (the "Climate Target Plan") in September 2020. This has received widespread attention: it proposes to increase the 2030 target to at least 55% emissions reduction by 2030.
How will this impact renewables and energy efficiency targets?
We will not know this with certainty until relevant EU legislation is reviewed. The impact assessment considered a range of policy scenarios aimed at achieving emissions reductions of circa 55% by 2030 and indicated what they implied for various targets and sectors. Based on this the Climate Target Plan states:
renewable energy would meet 38% to 40% of gross final consumption in 2030, and
energy consumption would further reduce in 2030, achieving savings of 36-37% (final energy consumption - total energy consumed by end users) and 39-41% (primary energy consumption – total energy used to meet final energy needs).
What are key policy and legislative tools for achieving this?
A proposed Regulation referred to as the EU Climate Law has recently undergone its first reading in the European Parliament. It seeks to establish a "framework for the irreversible and gradual reduction of greenhouse gas emissions and enhancement of removals by natural or other sinks in the Union". It would bind the EU institutions and Member States to take necessary actions to achieve carbon neutrality by 2050 and would require the Commission to monitor progress and take appropriate enforcement action where targets are not being met. It also amends the Governance Regulation to factor the new carbon neutral target into Member States' current climate policy planning and reporting obligations.
During its scrutiny of the proposed law, the Parliament in October 2020 voted to up the 2030 target to 60%, and urged the Commission to explore options for setting 2040 targets and negative post-2050 targets. The Parliament also sought a greater role in setting the indicative trajectory for achieving the target (against which EU and national progress can be measured and corrective adjustments made), a Union carbon budget, and a more explicit focus on emissions in the maritime and aviation transport sectors.
It will be interesting to see the enacted form of this key proposal. The robustness of its monitoring and enforcement mechanisms may be as determinative of future progress as the emissions reduction target it ultimately sets.
What else is planned?
Implementation of the EGD will require a more widespread revamp of existing legal measures. As planned under the EGD (and provided in the draft EU Climate Law) the Commission will assess by June 2021 how EU legislation needs to be revised. This will likely mean amendments to a range of instruments including the:
EU ETS Directive 2003/87/EC, which provides for caps on emissions of certain installations (mainly in power and industry) and sets an EU-wide emissions reduction target,
Effort Sharing Regulation (EU) 2018/842, which establishes emissions reduction targets for the EU and for Member States for sectors not included in the EU ETS (such as transport, buildings, agriculture, waste),
Land Use Regulation (EU) 2018/841, which requires equivalence as between emissions from land use and removal of emissions,
Renewables Directive (EU) 2018/2001, which sets the EU target for the percentage of energy demand to be met by renewable power,
Energy Efficiency Directives 2012/27/EU and (EU) 2018/2002, which set the EU targets (and requires Member States to set indicative contributions) for reducing energy consumption through increasing energy saving and efficiency,
Energy Taxation Directive 2003/96/EC, which provides for restructuring of the Community framework for the taxation of energy products and electricity, and
Trans-European Network-Energy and Transport Regulations, which have as their objectives the development and interoperability of trans-European networks.
The direction of travel is outlined in a series of strategies and plans referenced in the EGD Communication and Climate Target Plan which include the Energy Integration Strategy, the Methane Strategy, the Offshore Renewable Energy Strategy, the Hydrogen Strategy, Renovation Wave, the Industrial Strategy, the Circular Economy Action Plan, and the EU Strategy on Adaptation to Climate Change.
The immense scale of ambition of these proposals should not get lost in the detail. According to the Climate Target Plan, investment in the energy system, including transport, needs to increase over the period 2021-2030 by an additional ?350 billion on average each year (compared to 2011-2020) in order to achieve 55% reductions by 2030.
The investment pillar of the EGD is the EGD Investment Plan which aims to mobilise at least ?1trillion. Other cornerstone EU policies - notably the Sustainable Finance Package and the Capital Markets Union - are developing frameworks to facilitate re-direction of private investment towards sustainable and decarbonised materials, processes, products, services, and infrastructure, and to facilitate the use of market-based financing, securitisation and other funding alternatives to meet the financing requirements of those working to implement the EGD's goals. (Our briefings related to these topics are here, here and here.)
Developments in Ireland
We noted in our July 2020 briefing the extraordinary level of policy ambition in Ireland's new Programme for Government and the 2019 Climate Action Plan. In short, targets in the Programme for Government include an average 7% annual reduction in greenhouse gas emissions over the years 2021-2030, which equates to a reduction of 51% over the decade. There is a target of meeting 70% of electricity demand by renewables by 2030. (It is also worth noting that Ireland recently published its national climate and energy plan in accordance with the EU Governance Regulation and, in September 2020, the European Commission published its assessment of NECPs.)
The Programme for Government committed to publishing a Bill to amend the Climate Action and Low Carbon Development Act 2015 (the "2015 Act") to give legislative underpinning to Ireland's 2050 zero net emissions target and the core objectives of the Climate Action Plan.
The Bill – the Climate Action and Low Carbon Development (Amendment) Bill 2020 – has now been published. The key provision obliges the State to "pursue the transition to a climate resilient and climate neutral economy by the end of 2050". "Climate neutral economy" means "a sustainable economy, where greenhouse gas emissions are balanced or exceeded by the removal of greenhouse gases". This obligation is called the "national 2050 climate objective", and it replaces the 2015 Act's "national transition objective".
The Bill proposes a detailed framework for climate governance aimed at achieving the national 2050 climate objective as follows:
annual revisions to the Climate Action Plan, to take account of the carbon budget programme and to set out a roadmap of actions;
long term climate action strategies, which focus on sector specific emission reductions and removals, and which link in with the EU framework under Article 15 of the Governance Regulation;
national adaptation frameworks, which focus on reducing vulnerability of the State to negative effects of climate change and availing of any positive effects;
sectoral adaptation plans, to specify the adaptation policy measures that each Minister, having regard to the approved national adaptation framework, proposes to enable adaptation to the effects of climate change in the field concerned; and
carbon budgets. A "carbon budget" will be the total amount of greenhouse gas emissions permitted during the budget period. It will be proposed by the Climate Change Advisory Council ("CCAC"), finalised by the Minister for the Environment, Climate and Communications, and approved by the Government. The first budget period would commence from the start of 2021 for a period of five years. The "decarbonisation target range" will be the "target range of greenhouse gas emissions that are permitted in different sectors of the economy within the limits specified in the carbon budget".
There is an expanded list of matters to which the Minister and Government must have regard in making and approving these strategies and plans. They include international and EU climate commitments, Government policies, climate justice, emissions data, science and technology, recommendations of the CCAC, and more.
Further amendments deal with membership of the CCAC and require the CCAC to establish an Adaptation Committee. The CCAC's function of advising and making recommendations to Ministers and the Government is expanded in line with the new governance framework. The CCAC's obligation to report on progress each year also is framed in more detail.
A new section on Climate Reporting requires Ministers to attend and report on progress before a joint committee of the Oireachtas following which the committee may make recommendations to which the relevant Minister must respond.
There are new obligations for local authorities. They must make five year local authority climate action plans which specify mitigation and adaptation measures. They must have regard to these when making a development plan within the meaning of the Planning and Development Act 2000.
What level of detail can we expect from these plans and strategies?
A key purpose of climate governance frameworks is to ensure effective opportunities for the public, investors, regulators etc. to participate in the preparation of long-term strategies and plans.
Internationally, there is a trend of challenging the fitness for purpose of climate and energy policies before the courts. In Ireland, the Supreme Court in July 2020 struck down the current National Mitigation Plan for lack of the specificity required to provide transparency as to Government policy and to comply with the legislation pursuant to which it was made (namely the 2015 Act). (See the judgment in Friends of the Irish Environment CLG v The Government of Ireland, Ireland and the Attorney General.) The Court considered that the purpose of requiring the Plan to be specific was to allow any interested member of the public to know enough about how the Government intended to meet the 2015 Act's national transition objective so as to inform their decision as to whether the policy would be effective and appropriate.
This judgment will help to add momentum to the increasing sophistication of climate policy in Ireland. Development of energy and climate policy over the next decades will, by necessity, be iterative and collaborative (as is implicitly recognised by the Bill), but will also require adequate detail to enable all stakeholders to coordinate and progress the best solutions for implementation of such policy.
This article contains a general summary of developments and is not a complete or definitive statement of the law. Specific legal advice should be obtained where appropriate.
Alex McLean
Karen Killoran
Deborah Spence
Danielle Conaghan
Matthew Dunn
Nicole Ridge
Dearbhaile O'Brien
Katrina Donnelly
Ireland Energy and Natural Resources Energy Law Renewables Environment Climate Change Government, Public Sector Fiscal & Monetary Policy
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A Brief Analysis Of The 2020 Amendments Of The Turkish Energy Acts
Balcioglu Selçuk Ardiyok Keki Attorney Partnership
In Turkey, policymakers and technocrats have been united in adopting "domestic and national" energy policies.
Enerji Kanunlarında Değişiklik Yapan Kanunun Getirdikleri
Bununla birlikte, umudu son raunda kadar taşıyabilmenin yolu güçlü ve istikrarlı enerji politikalarının benimsenmesinden geçtiğini ifade etmek gerek.
Brexit: The EU-UK Trade And Cooperation Agreement And Energy On The Island Of Ireland
Given that electricity and gas systems on the island of Ireland are physically connected to those of GB, clarity on post-Brexit rules for trading across these systems is important to the energy sector here.
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EPC Contracts In The Energy Sector
Kolcuoglu Demirkan Kocakli Attorneys at Law
An engineering, procurement and construction ("EPC") contract is a complex form of construction contract, commonly used in large-scale construction works of complex infrastructure projects.
UK Offshore Wind Conference 2020 (Video)
As part of the Build Back Greener plan, the UK Prime Minister, Boris Johnson, announced the government's increased commitment to offshore wind in October 2020.
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Dose of Buffa
One Man's Thoughts
About Dan Buffa
St. Louis Cardinals Classic Rants
By D. Buffa Posted on December 13, 2013 April 12, 2017
Sons of Anarchy: Sopranos Meets Hamlet
Feeling the need to get a show to catch up on and enjoy? I have one for you. Sons of Anarchy isn't just a show about a group of criminals on bikes who hold the reins of a town called Charming in California. It's much more than that and creator/writer/cast member Kurt Sutter sprinkles in Shakespearean themes and blunt violence to remind viewers what they are watching is fresh, original and genuinely demented. Think of "Sopranos on Motorcycles wrapped inside a Greek Tragedy" and you have this FX network pulpy drama.
It is one of FX's best and most popular shows because it hasn't worn down after 6 seasons of action and the storytelling methods from Sutter and his writing team are unpredictable and heartbreaking at the same time. The 6th season wrapped last night in truly tragic and powerful fashion, and this film-addict is still uncoiling from the emotional trauma of the 2 hour finale experience. Sutter and his team aren't afraid to shock viewers with a major character death and did that on Tuesday night.
Sure, you can't convince Breaking Bad fanatics to consider a different kind of creative poison these days when it comes to explosive finales, but allow me to tell you why Sons is one of the most tragic, brilliant and bleak TV shows. This is a show you need to binge watch.
Put this show in the category of "antihero adoration" because the lead protagonist, Jax Teller(brilliantly played by Charlie Hunnam) is far from a good natured man but it's his sense of family and loyalty that keep us rooting for him while he commits/agrees to murderous criminal behavior. His struggle with power and how to swing it as he works his way through the criminal lay of the land sets the tone for the series.
Teller lives in the same neighborhood as Walter White and Tony Soprano but carries youth on his side. Men who surround themselves with family and rely on those ties to keep their soul a little less dark. This is what makes the show work so well. Sutter handled this material while writing for The Shield and knows how to create troubled men and women who do bad things but redeem themselves with their vulnerabilities, ignorance of evil and the honor shown in bringing peace to the future.
Sutter's casting is impeccable. Hunnam, Ron Perlman, Kim Coates, Tommy Flanagan, Mark Boone Junior, Theo Rossi, and Ryan Hurst make up the heart and soul of the show's club, SAMCRO(Sons of Anarchy Motorcycle Club Redwood Original). All of these actors are character actors ripped from careers spanning hundreds of films but locked in tightly on this show. The work of Hurst as Opie, Jax's right hand man and confidant, stands out due to the effect the character has on our protagonist.
In the 6th season, Jax and the Sons are aiming to cleanse themselves of the gun trade and move into more legit practices of income but when a school shooting brings down the wrath of the FBI and the gun used is traced back to them, all hell breaks loose. This is a rundown of every season. Jax steers the club towards safer waters, but their past and actions reel them back into hell. Sutter's marvel lies in his way of masking certain plot points with male camaraderie and small doses of humor. You don't see a big death coming and even if you do, the manner in which it happens is poetic and tragic. On Tuesday's season finale, a main character was killed off and with the 7th season setting up to be the last, the death will spring all kinds of creative life on the show. Each season, a couple major characters are killed off or a few characters' are turned around. The way television shows stay fresh is writing creatively and making no character safe. Without a net to catch you creatively, the show constantly gets fresh air. Far too many shows write with limited ambition and thus run out of gas quickly. Shows on FX like Rescue Me, Justified and The Shield ran so long because they are creatively limitless and any character can be put in jeopardy. No show does this tactic better than Sons of Anarchy.
Katey Sagal and Maggie Siff(Gemma and Tara) are the two female voices on the show, playing Jax's mother and wife, respectively. This is where the Hamlet themes come into play. The effect and influence of women on the kings that serve the land is heavy material to work with, but Sagal and Siff are pros. Gemma and Tara are set on a collision course for ownership of Jax's soul from the very first episode of Season 1, and in the 6th season, that internal battle comes to a bloody and furious head. If the finale of this season doesn't leave you gushing for air and ready to hit a punching bag, I am not sure what show will. Sutter pulls zero punches because he isn't dealing with real history here and has placed his characters in a dangerous world of envy, power, violence, loyalty and the hazards of mixing business with pleasure. Sagal and Siff are both Emmy worthy because they don't rely on gimmicks or melodrama to play women who are fiercely independent and highly dangerous women on a show dominated by men. If you are one of the critics of shows who hate the underuse and underwritten roles for women, check out this show.
Special mention must go to Dayton Callie, who plays Sheriff and SAMCRO ally Wayne Unser. Playing a character holding enough guilt and internal struggle for a warehouse full of older men, Callie is a Scottish born actor who does his best work right here. Like many of the cast members, the work of the actors on this show will overshadow whatever they have done or will do after this show ends next year. Look at Sagal's work here as the string pulling mother, and you won't see the goofy mom from Married With Children. Hunnam, Hurst and Flanagan have done various films but achieved nothing like the status they have gained through this show. If anyone is memorable outside of SOA, it is Perlman due to his heavy dosage of film work and his role in the Hellboy series. The cast is synonymous with the roles on the show and that is a big reason it works so well. Guest stars like Jimmy Smits, Peter Weller and Adam Arkin only help the action.
Should you watch this show right now? Yes, because it blends action, drama, blunt storytelling and a realistically bleak tone that proves to be addicting. Sutter paints dread all around the exterior of the story because he never wants the viewer to forget the mistakes and weight of guilt that the characters walk around with. These aren't good people but they are interesting and worth following. If you miss Sopranos, watch this show. If you want something that works faster than Boardwalk Empire or Ray Donovan, watch this show. If you want a show that holds up creativity wise (not Dexter), watch it now.
Kurt Sutter aims to please here but torments your soul long after the finales rest. He makes use of every detail of the plot in crafting his twists and reveals. A sink full of water and dishes, a love of a man for a woman he can't have, the effect of kids on a man's decision and the length bad men run in order to be track down their soul. You never forget what you are watching because the plot never slows down or gets too neat. This is a show about how actions lead to bad things and how the amount of lies told can lead to a blunt clarity no one can handle. Hunnam's work here is the heart and soul of the show. The actor can do more with a cold stare than most can do with three paragraphs. His trek through the 7th season is worth sitting down tonight and catching up. The best way to find out what the fuss is all about is to get a little dirty, watch and find out for yourself.
Brew a few pots of coffee, find a trusted brand of frozen pizza and settle in for the ride of your life with Sons of Anarchy. It may not be an HBO or Showtime production, but as Mad Men and Breaking Bad have proved, there is a fine slice of television being performed on AMC and FX. Once Sopranos wrapped up, everyone needed a fix for the criminal enterprise of entertainment. SOA has filled that gap just fine and hasn't lost a step in its 6 seasons.
Reach me at buffa82@gmail.com and @buffa82 on Twitter for comments, feedback and thoughts. Any response is appreciated.
-DLB
Categories: TV Show ReviewsTags: Charlie Hunman, FX, Kurt Sutter, Sons of Anarchy
Published by D. Buffa
A regular guy who feels a journalistic hunger to tell the news. I blog because its wired into my brain to write what I think in print. I offer an opinion. A solo tour here. Take regular stories and offer my spin on them. Sports, film, television, music, fatherhood, culture, food, and so on. Commentary on everything. A St. Louis native and Little Rock resident who wants to write just to keep the hands fresh and ready.	View all posts by D. Buffa
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It's that time of year again where supporters of a great cause can win a brand new home! The St. Jude Dream Home Give Away is back. Tickets go on sale Wednesday, September 2nd. A 100-dollar ticket gives you a chance to win the $450,000, four bedroom, two and a half bath home, under construction in Green Valley Ranch. And if you purchase a ticket on the first day of sales, you'll be entered to win a Bronco's replica helmet, signed by Peyton Manning! The goal is to sell 13-thousand tickets, raising 1.3 million dollars for St. Jude Children's Research Hospital.


text:
Man and two boys charged with murder of Daniel Laskos in Harold Wood
Jon King
Updated: 11:50 AM May 18, 2021
Daniel Laskos died on May 7 in Harold Wood. - Credit: Met Police
Detectives have charged a man and two boys with the murder of Daniel Laskos in Harold Wood.
Daniel was fatally stabbed in Church Road on May 7 not far from Amy's Park.
The police were called at 6.40pm to reports of a fight involving a number of people.
Officers attended and found 16 year-old Daniel with a stab wound. He was pronounced dead at the scene just after 7pm, according to the Met.
A 15-year-old boy was arrested on May 7, and was subsequently charged with murder and possession of an offensive weapon yesterday (May 12). He cannot be named for legal reasons.
Joshua Kerr, 18, and Callum Hands, 19 - both of Romford - were arrested on May 7 and May 9 respectively.
The pair were also charged with murder and possession of an offensive weapon yesterday.
5 Company dismisses 'unscrupulous individuals' reportedly caught flytipping in Rainham
6 Men jailed for using explosives in string of ATM thefts
7 Confirmed: Rush Green Post Office set to move
8 Romford accountant pleads guilty to 'calculated' £160k tax fraud
9 Man dumps knife amid Hornchurch police chase
10 Construction company asks to make changes to approved 40-flat development in Romford
All three appeared at Barkingside Magistrates' Court on Wednesday, May 12 where they were remanded in custody to appear at the Old Bailey this Friday (May 14).
Three other people had been arrested in connection with the incident. The first, a 16-year-old boy, was arrested on May 7 on suspicion of affray.
The second, an 18-year-old man, was arrested on Monday, May 10 on suspicion of murder.
The third, a 24-year-old man, was arrested on Tuesday, May 11 on suspicion of murder.
All three have been released on bail to return at a date in early June.
Detectives continue to investigate and are appealing for anyone with information to call police on 101 or tweet @MetCC.
Alternatively, information can be provided to Crimestoppers, anonymously by calling 0800 555 111.


text:
\section{Introduction}
Gauge theories are fundamental in many contexts of modern physics. \emph{Gauge invariance} is the manifestation of a local symmetry whose transformations act only on  a  small local set of degrees of freedom. Lifting a global symmetry of a matter theory to be local, usually  through the well-known \emph{minimal coupling} procedure, introduces \emph{gauge fields}. They account for the local symmetry and mediate the interactions between matter particles. Such theories may be found in the standard model of particle physics, including, for example, Quantum Electrodynamics (QED), with an Abelian gauge (symmetry) group,  or Quantum Chromodynamics, describing the strong nuclear force, with an $SU(3)$ symmetry.

While QED is weakly interacting and may be studied accurately using perturbation theory, QCD is very different. Due to its running coupling, in high energies limits it is very weakly coupled (asymptotically free), enabling perturbative treatment. Low energy QCD, however is a strongly interacting, non-perturbative theory. Among the important problems  of non-perturbative QCD is the \emph{confinement of quarks}, the responsible for binding quarks together into hadrons, whose breaking requires an infinite amount of energy, forbidding the existence of free quarks in the spectrum.

Back in the 1970s, lattice gauge theory (LGT) was proposed as an approach to deal with this problem \cite{wilson_confinement_1974}. What started as an analytical tool \cite{wilson_confinement_1974,kogut_hamiltonian_1975,polyakov_quark_1977} quickly emerged into an impressive numerical framework, in a combination with Monte-Carlo methods. That has given rise to many important QCD results and is still being used these days for static properties such as the hadronic spectrum \cite{aoki_flag_2020}. However, these computations are carried out in Wick-rotated Euclidean spaces, which blocks the road to direct obeservation of real-time dynamics as well as suffers from the sign problem in important finite chemical potential scenarios \cite{troyer_computational_2005}.

In the last decade, in parallel to the successful application of quantum information and technology based methods, such as quantum simulation \cite{feynman_simulating_1982} or tensor networks \cite{orus_practical_2014,cirac_matrix_2020} to many body models in condensed matter physics, the effort to generalise these methods to particle physics has begun \cite{wiese_ultracold_2013,zohar_quantum_2016,dalmonte_lattice_2016,preskill_simulating_2018,banuls_simulating_2020,banuls_review_2020}. Quantum simulation of LGTs, their mapping into controllable quantum platforms that are controllable in the lab, allowing one to experimentally study inaccessible physics, has evolved from the early theoretical proposals of analog simulators \cite{zohar_confinement_2011,banerjee_atomic_2012}, digital ones \cite{buchler_atomic_2005,tagliacozzo_optical_2013} or quantum computer algorithms \cite{byrnes_simulating_2006} into an experimental field \cite{martinez_real-time_2016,kokail_self_2019,schweizer_floquet_2019,mil_scalable_2020,yang_observation_2020}, attracting particle and nuclear physicists \cite{cloet_opportunities_2019} who now consider it to be a valid computational method.

In this article we will address the challenges faced by the quantum simulation of LGTs, from the theoretical point of view, in particular in more than one space dimension (which has so far been less explored experimentally). In the following sections, we will provide some basic introduction to the theories in question, formulate a list of requirements which must be satisfied, bypassed or overcome in such simulators and discuss them.

 \section{Degrees of freedom, Hilbert Space, Symmetry}

 When discussing the quantum simulation of a physical model, a proper map needs to be devised between the simulated model and the simulating platform. This map can be exact (in the ideal, almost eutopic case) or approximate (with proper error bounds and accuracy estimations). The simulation can be \emph{analogue}, involving a mapping of the Hamiltonian; \emph{stroboscopic} or analogue-digital, in which different parts of the Hamiltonian are implemented sequentially, using short time pulses similar to quantum gates, based on the Trotter-Suzuki expansion \cite{suzuki_decomposition_1985} and possibly involving ancillary degrees of freedom; or completely \emph{digital}, implementing the dynamics via a non-universal quantum circuit. But what all these approaches share is that one needs the simulator to encode the degrees of freedom, the Hilbert spaces, the symmetries and the interactions of the simulated model, whatever choice is made for the simulation approach. Those ingredients of the simulated model thus need to be carefully examined, before one can practically reconstruct the model using other building blocks. And the closer the available elementary blocks and interactions of the simulating platform are to those of the simulated model, the better the quantum simulator is. These arguments are fundamental when one considers the design of a quantum simulator, and they lead to proper choices of the simulating platform, the simulation approach and the mapping method. We will thus begin our discussion with a general review of the ingredients of a lattice gauge theory and the requirements they impose on their quantum simulation - in particular in more than a single space dimension.

Following the Hamiltonian approach to LGTs \cite{kogut_hamiltonian_1975}, we only discretize space, and time is a continuous, real coordinate. The lattice sites, hosting the matter fields (usually fermionic, but can be bosonic too) are labelled by $\mathbf{x}\in\mathbb{Z}^d$. $\left\{\mathbf{e}_i\right\}_{i=1}^d$, are unit vectors in the positive directions. The links, which hosts the gauge field degrees of freedom, are denoted by pairs of a starting site and a direction, $\left(\mathbf{x},i\right)$.

This immediately brings us to the first requirement from an LGT quantum simulator: it should include two different types of degrees of freedom - gauge field and matter, residing on the links and the sites, respectively. In the most general settings, one needs to consider a quantum simulation platform which enables the interplay of fermionic and non-fermionic degrees of freedom - e.g. ultracold atoms in optical lattices \cite{jaksch_cold_1998}. Other platforms without fermions (e.g. trapped ions or superconducting qubits) may be used (i)
when pure gauge theories (without matter) are simulated,  or when the matter is bosonic; (ii) in a single space dimension, where fermionic
matter may be mapped conveniently to spins, using the Jordan-Wigner map \cite{jordan_uber_1928}, such as in \cite{martinez_real-time_2016,yang_observation_2020,davoudi_towards_2020,atas_su_2021}); (iii) when the fermionic matter is mapped, using the gauge field which allows that in some cases, to hard-core bosonic matter \cite{zohar_eliminating_2018} (this can be done locally and unitarily, and in some cases the matter may be completely eliminated \cite{zohar_removing_2019}). Finally, one may also use only fermionic degrees of freedom, when constructing all the gauge field operators by auxiliary fermionic modes residing on the links \cite{brower_qcd_1999}, as used e.g. in \cite{banerjee_atomic_2012,banerjee_atomic_2013}.

Gauge transformations are in the centre of gauge theories. They are parametrised by elements of the \emph{gauge group} $G$, which is usually a compact Lie group (in particle physics scenarios) or a finite one (in several condensed matter contexts). On each site $\mathbf{x}$ one defines the unitary gauge transformation operators $\hat{\Theta}_g\left(\mathbf{x}\right)$ for each $g \in G$, acting only on a finite volume of space - the matter degree of freedom at $\mathbf{x}$, and the gauge fields on the links intersecting in it.  A state $\left|\psi\right\rangle$ is gauge invariant if
\begin{equation}
	\hat{\Theta}_g\left(\mathbf{x}\right) \left|\psi\right\rangle = \left|\psi\right\rangle \quad \quad \forall \mathbf{x} \in \mathbb{Z}^d , g \in G
	\label{psitrans}
\end{equation}
(but not only if; we disregard here the case of \emph{static charges}, a discussion of which may be found in \cite{kasper_from_2020}). An an operator $O$ is gauge invariant if and only if
\begin{equation}
	\hat{\Theta}_g\left(\mathbf{x}\right) O 	\hat{\Theta}^{\dagger}_g\left(\mathbf{x}\right) = O  \quad \quad \forall \mathbf{x} \in \mathbb{Z}^d , g \in G
	\label{Otrans}
\end{equation}

This allows us to formulate the second requirement: Quantum Simulators of lattice gauge theories should be gauge invariant - that is, manifest a local symmetry parametrised by the gauge group $G$. Gauge transformations $\hat{\Theta}_g\left(\mathbf{x}\right)$ should be well defined on each site $\mathbf{x} \in \mathbb{Z}^d$ and for any $g \in G$; the system has to be prepared initially in a gauge invariant state $\left|\psi\right\rangle$ as in Eq. (\ref{psitrans}); and the dynamics should include gauge invariant interactions. Normally, such symmetries are not available for free in the simulating platforms, and one has to impose them or map them to an existing symmetry of the simulating platform, if possible.

To discuss all that more concretely, let us zoom into the properties of the matter and gauge field Hilbert spaces.

\section{Matter Fields}
The matter degrees of freedom in most LGTs, especially in particle physics context, are fermionic. In which case, on each site $\mathbf{x}$ we introduce a set of fermionic creation operators, $\psi^{\dagger}_m\left(\mathbf{x}\right)$. In general, the indices carried by the fermionic operators may label spin (related to the Lorentz group), flavour or colour (related to the gauge symmetry). There are different methods for dealing with fermions on a lattice, having to do with the doubling problem \cite{kogut_lattice_1983} which we shall not discuss here. In some LGTs, however, bosonic matter or first-quantised, spin-like matter, may be considered as well.
For simplicity, in many quantum simulation works the staggered fermions formulation \cite{susskind_lattice_1977} is used: the spin components are distributed over several lattice sites,  recombined into spinors in the continuum limit. In this case, less fermionic species need to be considered on each site, which eases the technological demands from the simulator. Nevertheless, works on simulation of other fermionic formulations, such as naive \cite{zohar_simulating_2013} or Wilson fermions \cite{zache_quantun_2018}.

Flavour indices may be introduced when multi-flavour physics is studied, and in most cases this may only have experimental consequences having to do with the inclusion of more fermions and making sure that they all interact in the desired way; from the theoretical point of view of constructing a model or its simulation, the generalisation from one flavour to more is straight-forward and hence will not be discussed here. Finally, we are left with the colour indices, having to do with the gauge symmetry.

The modes $\psi^{\dagger}_m\left(\mathbf{x}\right)$ on each site form a complete spinor in a given representation of the gauge group $G$, mostly an irreducible one (irrep). That implies that when Abelian groups, such as $U(1)$ and $\mathbb{Z}_N$ are considered, we will only have one fermionic mode per site, $\psi^{\dagger}\left(\mathbf{x}\right)$. In non-Abelian cases, this spinor will correspond to a higher-dimensional irreducible representation - e.g. the fundamental one with dimension $N$ (and hence $N$ fermionic components) for $SU(N)$ or $U(N)$. Let us restrict ourselves to this choice, for simplicity; we then define local unitary transformations  $\theta_g\left(\mathbf{x}\right)$ parametrised by the group elements, for which
\begin{equation}
\theta_g\left(\mathbf{x}\right) \psi^{\dagger}_m\left(\mathbf{x}\right) \theta_g^{\dagger}\left(\mathbf{x}\right) =
\psi^{\dagger}_{m'}\left(\mathbf{x}\right)D_{m'm}\left(g\right)
\end{equation}
where $D\left(g\right)$ is the unitary representation of $g$ in the irreducible representation picked for the matter. When $G$ is a compact Lie group, its elements $g$ are completely determined in terms of group parameters, or coordinates on the group manifold, $\phi_a\left(g\right)$. Then, we may use the generators (local charge operators) $Q_a\left(\mathbf{x}\right)$, satisfying the group's algebra
$
	\left[Q_a\left(\mathbf{x}\right),Q_b\left(\mathbf{y}\right)\right]=i\delta\left(\mathbf{x},\mathbf{y}\right)f_{abc}Q_a\left(\mathbf{x}\right)
$,
where $f_{abc}$ are the group's structure constants, to express the transformation,
$
	\theta_g\left(\mathbf{x}\right) = \exp\left(i \phi_a\left(g\right) Q_a\left(\mathbf{x}\right)\right)
$.
In the case of fermionic matter, we can express the local charges as bilinears of the mode operators, e.g.
$
	Q_a\left(\mathbf{x}\right) = \psi^{\dagger}_m \left(\mathbf{x}\right) \left(T_a\right)_{mn}
	\psi_n \left(\mathbf{x}\right)
$
, where $T_a$ are the suitable matrix representations of the generators, with
$
	\left[T_a,T_b\right]=if_{abc}T_c
$
(with some modifications depending on the fermionic prescription used, for example see \cite{zohar_formulation_2015} for the staggered case).

\section{Gauge Fields}
In the continuum, gauge fields are bosonic; their excitations are countable particles, such as photons and gluons, which are described within bosonic Fock spaces. On the lattice, however, the gauge fields are rather \emph{first quantised} objects, described in terms of simple Hilbert spaces on the links, rather than Fock spaces with particle excitations. Let us see that.
 On each link of the lattice, the gauge field Hilbert space may be spanned in terms of two convenient bases (among others). We shall postpone the discussion of one of those, \emph{the representation basis}, to later, and introduce now the other one - the \emph{group element basis}. As implied by its name, the elements of this basis are labelled by elements of the gauge group - $\left\{\left|g\right\rangle\right\}_{g\in G}$. When $G$ is finite, we denote by $\left|G\right|$ the number of its elements, and this is the \emph{finite} dimension of the Hilbert space we have on each link (for example, when $G=\mathbb{Z}_N$, the group elements may be identified with the $N$th roots of $1$, and $\left|G\right|=N$). The basis states then satisfy the orthonormality relation
\begin{equation}
	\left\langle g | h\right\rangle = \delta_{gh}
	\label{orth}
\end{equation}
with the Kronecker delta.
When $G$ is a compact Lie group, $\left|G\right|$ denotes the group's volume, defined by $\left|G\right|=\int dg$ - integration of the group's Haar measure $dg$ over the whole manifold; $\delta_{gh}$ will hence be a distribution.

We realise that the on-link gauge field Hilbert spaces of a lattice gauge theory are first quantised, and do not require the use of any second-quantised, Fock space objects. However, in the case of infinite groups (e.g. compact Lie ones), these Hilbert spaces are infinite, which might be problematic to implement on the simulation platforms. We will discuss truncation schemes below.

Since each link is connected to two sites, on which two differend, independent gauge transformations may be defined, the gauge field on a link can be affected by two independendent gauge transformations, associated with either of its ends. We thus define unitary operators $\Theta_g\left(\mathbf{x},i\right)$ and $\tilde\Theta_g\left(\mathbf{x},i\right)$ acting on the gauge field on the $\left(\mathbf{x},i\right)$ link, transforming it from the right and left sides respectively; in the group element basis, they have a simple interpretation as group multiplication operators,
\begin{equation}
	\Theta_g \left|h\right\rangle = \left|hg^{-1}\right\rangle  \quad \text{ and } \quad \tilde\Theta_g \left|h\right\rangle = \left|g^{-1}h\right\rangle  \quad \forall g,h \in G
\end{equation}
We also define unitary transformation opeartors for the matter degrees of freedom on the sites, $\theta_g\left(\mathbf{x}\right)$. Its explicit definition depends on the nature of the matter. Altogether, the local gauge transformation at $\mathbf{x}$ parametrised by $g$ is implemented with the unitary
\begin{equation}
	\hat{\Theta}_g\left(\mathbf{x}\right) = \overset{d}{\underset{i=1}{\prod}}\left[\tilde\Theta_g\left(\mathbf{x},i\right)\Theta^{\dagger}_g\left(\mathbf{x},i\right)\right]\theta^{\dagger}_g\left(\mathbf{x}\right)
	\label{Gtrans}
\end{equation}

When $G$ is a compact Lie group, we can express the operators $\Theta_g$ and $\tilde\Theta_g$ using generators and group parameters. Let us introduce two sets of generators, $\left\{R_a\right\}$ and $\left\{L_a\right\}$, generating the right and left transformations respectively:
\begin{equation}
	\Theta_g = e^{i\phi_aR_a}; \quad \tilde\Theta_g = e^{i\phi_aL_a}
\end{equation}
where $\left\{\phi_a\left(g\right)\right\}$ is the set of group parameters (coordinates) uniquely associated with $g$, and the generators satisfy the group's mutually indepdnedent right and left Lie algebras,
$
	\left[R_a,R_b\right]=if_{abc}R_c;$ $\left[L_a,L_b\right]=-if_{abc}L_c ;$ and $\left[R_a,L_b\right]=0$.
When $G$ is Abelian, left and right transformations are the same, all the generators commute and left and right transformations are the same. In the $U(1)$ case, for example, there is only one generator, $E=R=L$. In the $SU(2)$ case, there are two sets of "angular momentum operators", right and left, which in the rigid body picture may be seen as the angular momenta in the space and body frames \cite{kogut_hamiltonian_1975,kasper_from_2020}.

Hence, in the compact Lie case, the local gauge transformations are generated by the operators
\begin{equation}
	G_a\left(\mathbf{x}\right) = \overset{d}{\underset{i=1}{\sum}}\left(L_a\left(\mathbf{x},i\right)-R_a\left(\mathbf{x}-\mathbf{e}_i,i\right)\right)-Q_a\left(\mathbf{x}\right)
\end{equation}
and gauge invariant states satisfy
\begin{equation}
	G_a\left(\mathbf{x}\right)\left|\psi\right\rangle = 0 \quad \forall \mathbf{x} \in \mathbb{Z}^d, a
	\label{Gausslaw}
\end{equation}
(disregarding static charges again).
In the $U(1)$ case, we have $G\left(\mathbf{x}\right) = \overset{d}{\underset{i=1}{\sum}}\left(E\left(\mathbf{x},i\right)-E\left(\mathbf{x}-\mathbf{e}_i,i\right)\right) - Q\left(\mathbf{x}\right)$, and thus
\begin{equation}
	\overset{d}{\underset{i=1}{\sum}}\left(E\left(\mathbf{x},i\right)-E\left(\mathbf{x}-\mathbf{e}_i,i\right)\right)\left|\psi\right\rangle = Q\left(\mathbf{x}\right)\left|\psi\right\rangle
	\label{U1gauss}
\end{equation}
- the divergence of the gauge field operator $E$ on a site equals the charge  there $Q\left(\mathbf{x}\right)$. With this we immediately recognise $E$ as the \emph{electric field} operator on the link, and Eq. (\ref{U1gauss}) as the lattice \emph{Gauss law}; generalising to non-Abelian groups, we call $R_a$ and $L_a$ the right and left electric fields, respectively, and then (\ref{Gausslaw}) is the rather more general, non-Abliean form of the Gauss law.

\subsection{Imposing Gauge Invariance on a Quantum Simulator}
	 So far, several methods have been proposed for the imposition of gauge invariance in quantum simulators. The first is \emph{effective gauge invariance} - an analogue scheme, in which the desired gauge-invariant Hamiltonian is only implemented effectively. One implements, instead, a different, so-called \emph{primitive Hamiltonian} $H'$, violating the local symmetry ($\left[H',\hat{\Theta}_g\left(\mathbf{x}\right)\right] \neq 0$), but including penalty terms which constrain the symmetry.
For example, let us consider the first analogue schemes for Kogut-Susskind simulators \cite{zohar_confinement_2011,banerjee_atomic_2012,zohar_simulating_2012}, which discussed cold atomic implementations of a $U(1)$ theory (compact QED). It is an Abelian model whose gauge transformations are generated by a single operator $G\left(\mathbf{x}\right)$ on each site: $\hat{\Theta}_{\phi}\left(\mathbf{x}\right) = e^{i \phi G\left(\mathbf{x}\right)}$ for every $\phi \in \left[0,2\pi\right)$. As in (\ref{Gausslaw}), for a gauge invariant state $\left|\psi\right\rangle$,  $G\left(\mathbf{x}\right)\left|\psi\right\rangle=0$ on each site $\mathbf{x}$. If $H'$ contains  penalty terms of the form $\lambda\underset{\mathbf{x}}{\sum}G^2\left(\mathbf{x}\right)$, and $\lambda$ is significantly larger than any other energy scale in $H'$,  the spectrum will be split into sectors corresponding to eigenvalues of $G\left(\mathbf{x}\right)$. One can perturbatively derive an effective Hamiltonian not mixing these sectors, assuming that transitions between them are only possible virtually. As a result, in the lowest energy sector we will get an effective Hamiltonian with the local symmetry we wanted.

Usually, when the interactions in the primitive Hamiltonian are properly tailored, the second order is enough for the desired interactions (and the remaining, higher terms are still gauge invariant). The method, which can be extended to non-Abelian cases  \cite{banerjee_atomic_2013}, is considered slightly forced and less robust than others, since it is sensitive to experimental imperfections and requires very careful fine-tuning, especially in the non-Abelian cases where there are several $G_a$ operators on each site (e.g. three for $SU(2)$). Furthermore, although the $G_a\left(\mathbf{x}\right)$ operators are local, squaring them introduces interactions which may be hard to implement. More recently, however, it was shown that one may also use local constraints which are linear in the generators  - that is,  without interactions, in both the Abelian \cite{halimeh_gauge_2020} and non-Abelian (using dynamical decoupling) \cite{kasper_non_2020} cases. Another option to introduce constraints linearly is by using dissipation and non-unitary dynamics, utilising the Zeno effect to force gauge invariance \cite{stannigel_constrained_2014}.

Another analogue approach is \emph{symmetry mapping.} There, the local symmetry is guaranteed in  a more fundamental level. One maps (when possible) a symmetry of the simulating platform to the local symmetry of the simulated model. It was introduced in a proposal for simulating lattice gauge theories with ultracold atoms in optical lattices \cite{zohar_quantum_2013}, where the atomic states are classified by their hyperfine angular momentum, and the available interactions are two-atom collisions. The collision preserves the total hyperfine angular momentum, and thus, by properly choosing the hyperfine states playing different roles in the simulator - fermions on the sites for the matter and bosons, on the links (out of which the gauge field operators are constructed through through Schwinger representations), one may exactly map all the gauge invariant processes to angular momentum conserving collisions. This was further analysed  \cite{kasper_implementing_2017} and demonstrated experimentally by implementing a single building block \cite{mil_scalable_2020}. In another recent example for symmetry mapping, a local symmetry of a Rydberg atom state was exactly mapped to gauge invariance \cite{surace_lattice_2020}.

Finally, \emph{digital and stroboscopic implementations} offer various ways to impose gauge invariance: when the simulation does not involve a mapping of the Hamiltonian but rather an implementation of the time evolution by short time pulses implementing different interactions and Hamiltonian terms separately (trotterisation), possibly using auxiliary degrees of freedom, there are more options to enforce the symmetry. These range from tailoring gauge invariant interactions with an ancilla \cite{tagliacozzo_optical_2013,tagliacozzo_simulation_2012,zohar_digital_2017,zohar_digital_2017-1,bender_digital_2018,lamm_general_2019} to developing tools to encode the symmetries on quantum computer algorithms \cite{byrnes_simulating_2006,klco_quantum_2018,klco_su_2020,raychowdhury_loop_2020,ciavarella_trailhead_2021}. When such methods are used, it is important to monitor gauge invariance and its possible breaking. In some each step of the strobscopic dynamics preserves the symmetry \cite{zohar_digital_2017-1} and thus  trotterisation  does not affect the gauge invariance. More generally, some works have been written on monitoring gauge invariance in digital simulations, as in   \cite{stryker_oracles_2019}.

One may also deal with gauge invariance in the simulation, by completely bypassing it. The gauge symmetry implies some redundancy in the description of the physical state. To lift it one can use the local constraints to eliminate the matter or the gauge field degrees of freedom. Eliminating the gauge field degrees of freedom by solving the Gauss law is possible in a single space dimension \cite{martinez_real-time_2016}, but not in further dimensions. Eliminating the matter fields is possible, in some cases, in any dimension \cite{zohar_removing_2019}. The other way to lift the redudancy is to change to a dual formulation of gauge theories, with \emph{magnetic} variables, where there is no local symmetry anymore. Such formulations were introduced in the pure gauge case \cite{drell_quantum_1979,kaplan_gauss_2020,celi_emerging_2020} as well as in the presence of dynamical fermionic matter, using translational invariant, Green's function based approach \cite{bender_gauge_2020} or a maximal tree approach \cite{haase_resource_2020}.

\subsection{Gauge Field Bases}

As discussed, the gauge field Hilbert space on a link may be spanned by the group element basis states, $\left\{\left|g\right\rangle\right\}_{g\in G}$. These are the eigenstates of the group element operators, $U^j_{mn}$. Let $j$ be an irreducible representation of $G$, and $D^j\left(g\right)$ the $j$ unitary representation of the group element $g$. Then, we define
\begin{equation}
	U^j_{mn} = \int dg D^j_{mn}\left(g\right) \left|g \right\rangle\left\langle g \right|
\end{equation}
(where the integral is replaced by a sum if the group is finite). This is a matrix of operators acting on the link's Hilbert space, all commuting with one another, as can clearly be seen in this definition: they are all diagonal in the group element basis. It is straightforward to see that $\Theta_g U^j_{mn} \Theta^{\dagger}_g = U^j_{mn'}D^j_{n'n}\left(g\right)$ as well as  $\tilde \Theta_g U^j_{mn} \tilde \Theta^{\dagger}_g = D^j_{mm'}\left(g\right)U^j_{m'n}$ - the group element operator transforms like a unitary matrix representation of $G$; in the Lie group case these are equivalent to
$\left[R_a,U^j_{mn}\right] = U^j_{mn'}\left(T^j_a\right)_{n'n}$ and $\left[L_a,U^j_{mn}\right] = \left(T^j_a\right)_{mm'}U^j_{m'n}$, respectively. In the Abelian, $U(1)$ case, all the irreps are one dimensional, with $U^j = e^{ij\phi}$ for any integer $j$; the operator $\phi$ plays the role of the compact vector potential, and $\left[E,U\right]=U$ implies that it is canonically conjugate to $E$.

Another useful basis is the \emph{representation basis}, whose elements are eigenstates of the group transformation operators $\Theta_g$ and $\tilde\Theta_g$, or more specifically - of a maximal set of mutually commuting operators thereof. Its elements, $\left|jmn\right\rangle$, are obtainable from the group element states through
\begin{equation}
\left\langle g|jmn\right\rangle = \sqrt{\frac{\text{dim}\left(j\right)}{\left|G\right|}}D^j_{mn}\left(g\right)
\end{equation}
where $j$ labels an irreducible representation, with dimension $\text{dim}\left(j\right)$. In the case of a compact Lie group, one can recognise $j$ as the eigenvalue(s) of Casimir operator(s), and $m,n$ are, respectively, eigenvalues of the maximal set of mutually commuting $L_a$ and $R_a$ operators. When the group is abelian, all the irreducible representations are one dimensional, and hence there are no $m,n$ quantum numbers, and the representation states are eigenstates of the electric field operator, with integer spectrum $E\left|j\right\rangle = j\left|j\right\rangle$ (the Hilbert space of a particle on a ring, with coordinate $\phi$ and angular momentum $E$). The $SU(2)$ link Hilbert space is that of a rigid rotator \cite{kogut_hamiltonian_1975,kasper_from_2020}: the coordinate (group element) state may be parametrised by the three Euler angles, while the representation basis is given by angular momentum operators, responsible for rotations in the space ($R_a$) and body ($L_a$) frames: commuting rotations giving rise to the same total angular momentum (rotation scalar) $\mathbf{J}^2 = R_aR_a = L_aL_a$. Then we have $\mathbf{J}^2\left|jmn\right\rangle = j\left(j+1\right) \left|jmn\right\rangle$,
$L_z\left|jmn\right\rangle = m \left|jmn\right\rangle$ and $R_z\left|jmn\right\rangle = n \left|jmn\right\rangle$.

Generally speaking, in the non-Abelian case one can formally decompose the representation state into a product of a left state and a right state, $\left|jmn\right\rangle = \left|jm\right\rangle \otimes \left|jn\right\rangle$ carrying the same representation. This implies that although it may be tempting to divide the link of a lattice gauge theory into two different parts, the left and the right ones,  trasformed by the gauge transformations of the link's beginning and end, respectively, the two parts are not independent, and are constrained by having the same irrep $j$. Formally, the Hilbert space on a link may be written as
\begin{equation}
	\mathcal{H}_{\text{link}} = \underset{j}{\bigoplus}\left(\mathcal{H}_j\otimes\mathcal{H}_j\right)
	\neq \left(\underset{j}{\bigoplus}\mathcal{H}_j\right) \otimes \left(\underset{j'}{\bigoplus}\mathcal{H}_{j'}\right)
\end{equation}
(where $\mathcal{H}_j$ is the Hilbert space spanned by the multiplet $\left|jm\right\rangle$, with a fixed $j$) and one cannot simply decompose the link Hilbert space into a product of two (this is also manifested through the group element basis, which takes the link as a whole). There are several formulations of LGTs which do break the link into two (which may have exactly the advantage of coupling to two different Gauss laws) but then a constraint is imposed. Thus, when used for quantum simulation, one must make sure that the constraint between the two parts of each link is not violated, for example through introducing a penalty term forcing it into the Hamiltonian. This is done, for example, in the link model \cite{brower_qcd_1999}, used for several quantum simulation schemes (\cite{banerjee_atomic_2012,banerjee_atomic_2013,wiese_ultracold_2013} and more) or the prepotential approach \cite{mathur_loop_2007}, used for example in \cite{zohar_cold-atom_2013} and \cite{raychowdhury_loop_2020}. In another approach \cite{zohar_formulation_2015} the link is kept as a whole.

\subsection{Gauge Field Truncations}
Another possible issue when designing quantum simulators of LGTs has to do with the dimension of the link Hilbert spaces: when the groups are infinite, as in the compact Lie case, these Hilbert spaces are infinite, which may be somewhere between inconvenient and impossible for common quantum simulation platforms. Then, one can truncate the gauge field Hilbert spaces in a way that simplifies this problem - but, as usual, may raise other ones.

When truncating the gauge field Hilbert spaces, we keep only a finite number of states, either in the group element or representation basis. Each truncation has its own advantages and disadvantages, depending on the simulation scheme and goals. In the representation basis, it is easy to put a cutoff on the representations we use. It follows from the Clebsch-Gordan series that, in the representation basis, the group element operator takes the form
$
U^j_{mn} = \underset{J,K}{\sum}\sqrt{\frac{\text{dim}\left(J\right)}{\text{dim}\left(K\right)}}
\left\langle J M j m | K M \right\rangle
\left\langle K N | J N j n \right\rangle
$
which suggests an immediate truncation scheme \cite{zohar_formulation_2015}, in which we restrict our Hilbert space only to representation states of some representations, connected by nonvanishing Clebsch-Gordan coefficients. For example, in $SU(2)$ the smallest truncation is five dimensional, with the representations $j=0$ ($\left|000\right\rangle$) and $j=\frac{1}{2}$ (with ($\left|\frac{1}{2},\pm\frac{1}{2},\pm\frac{1}{2}\right\rangle$). The great advantage of such a truncation is that although the Hilbert space is truncated, the gauge group remains the original one: the truncated $U$ operator still has the same transformation properties under $\Theta_g$ and $\tilde\Theta_g$, for every $g \in G$. This is very useful when one wishes to impose the symmetry using penalty terms, with the original Gauss laws, or use the symmetry mapping techniques.

On the other hand, since we truncated the representation basis, its dual basis - that of group elements - cannot be used (and is ill defined) after the truncation, and one cannot use group elements to describe the Hilbert space any longer. Furthermore, the truncated group element operator is no longer unitary as a matrix, and its elements are no longer commuting operators, which blocks the way to some simulation schemes, such as the stroboscopic stator method \cite{zohar_digital_2017-1}, where these properties are crucial.

As for the physical implications of this truncations - they are not yet clear in all the physical scenarios and theories. The full Hilbert space limit is obviously obtained when the cutoff is raised until all the representations are included again; one may argue that the truncations only affect short range physics but become less and less significant when large scale properties are sought and blocking is considered;  and in the link model formulation \cite{brower_qcd_1999} one may introduce an extra compact dimension which, once integrated over properly, allows to obtain the continuum the full gauge theory in the continuum limit from a truncated model on the lattice. In any case, however, this truncation scheme allows one to implement physical models with the full gauge group, which are of great interest and exhibit rich physics even without having a proper continuum limit: this opens the way to the study of many interesting lattice gauge theories that have not been considered before \cite{banerjee_atomic_2012,tagliacozzo_simulation_2012,wiese_ultracold_2013,banerjee_atomic_2013} and now are within experimental reach \cite{surace_lattice_2020}.

Another option is to truncate in the group element basis: choosing a subset of group elements instead of the full group. When this subset is a subgroup, nice properties such as $U_{mn}$  being a unitary matrix and commutation of all its elements as Hilbert space operators are kept; however the gauge group is narrowed to a finite subgroup and the Gauss laws no longer exist, preventing for example the option of Gauss law penalty terms. This is very useful, however, when using the stator scheme \cite{zohar_digital_2017-1}.

The most ideal scenario for such a truncation would be to identify an infinite series of finite subgroups of our gauge groups, which converge to the full group. Then we could think of a series of quantum simulators, all exhibiting gauge invariance, converging to the full model whose results could be deduced via extrapolation techniques. While this is the case for $U(1)$, which is the infinite $N$ limit of $\mathbb{Z}_N$, this is not the case for other relevant groups, such as $SU(2)$ or $SO(3)$: the crystallographic restriction tells us that the number of relevant finite transformation groups is finite (and very small). Then, of course, a due question is whether we are actually interested in implementing some gauge symmetry or could think of a simulation scheme in which some group elements, not necessarily forming a group, are chosen for the simulation.

\section{The Hamiltonian}

The last important ingredient to consider is the Hamiltonian. Normally,  a lattice gauge theory is described by the Kogut-Susskind Hamiltonian \cite{kogut_hamiltonian_1975}, consisting of four parts - two free and two interacting.

The free parts include (i) the matter mass term, depending on local number operators. For example, in the case of staggered fermions in $d$ space dimensions, it will have the form
\begin{equation}
	H_M = M\underset{\mathbf{x}}{\sum}\left(-1\right)^{x_1 + ... + x_d}
	 \psi^{\dagger}_m\left(\mathbf{x}\right)  \psi_m\left(\mathbf{x}\right)
\end{equation}
and (ii) the electric energy term, consisting of projectors onto the representations of the gauge field states on the link,
\begin{equation}
	H_E = \frac{g^2}{2}\underset{\mathbf{x};i=1,...,d}{\sum}\underset{j}{\sum}f_j\left|jmn\right\rangle\left\langle jmn \right|_{\mathbf{x},i}
\end{equation}
where $g$ is the coupling constant.
In the compact Lie group case it will depend on the quadratic Casimir operator,
$	H_E = \frac{g^2}{2}\underset{\mathbf{x};i=1,...,d}{\sum}\mathbf{J}^2\left(\mathbf{x},i\right)$ (simply $E^2$ for $U(1)$) - resembling the well known continuum expression for electric energies.

The interacting parts include (i) the link interaction - hopping of fermions to neighbouring sites, minimally coupled to the gauge field on the link in the middle, ensuring the gauge symmetry. For example, it will take the form
\begin{equation}
H_{\text{int}}=\underset{\mathbf{x},i}{\sum}\left(\epsilon_i\left(\mathbf{x}\right)\psi^{\dagger}_m\left(\mathbf{x}\right)U_{mn}\left(\mathbf{x},i\right)\psi^{\dagger}_n\left(\mathbf{x}+\hat{e}_i\right) +h.c.\right)
\end{equation}
(where the tunneling amplitudes $\epsilon_i\left(\mathbf{x}\right)$ are chosen in a way the produces the right fermionic dispersion relation \cite{susskind_lattice_1977}), and the representation chosen for the group element operator is the same as that of the matter. Finally, we have (iv) the magnetic energy term, which is a four body interaction of all the links around each plaquette of the lattice. It is a complicated interaction term, which becomes free in the continuum limit (corresponding to the magnetic field squared, and hence the name magnetic energy) and does not exist in a single space dimension. It takes the form
\begin{equation}
	H_B = -\frac{1}{2g^2}
	\underset{\mathbf{x};i<j}{\sum}\left(\text{Tr}
	\left(
	U\left(\mathbf{x},i\right)
	U\left(\mathbf{x}+\hat{e}_i,j\right)
	U^{\dagger}\left(\mathbf{x}+\hat{e}_j,i\right)
	U^{\dagger}\left(\mathbf{x},j\right) + h.c.
	\right)\right)
	\end{equation}
where the trace is over the matrix indices of the group element operators, and is not needed in the Abelian cases.

This plaquette interaction is one of the biggest challenge of quantum simulators of LGTs in more than one space dimension. Such plaquette or ring exchange interactions were considered for condensed matter gauge theories in the past, e.g. in \cite{buchler_atomic_2005}. In the context of Kogut-Susskind Hamiltonian, there are several ways to implement them, which have not been implemented experimentally so far, as they are either complicated, or involve weak interactions, or both. Possible analogue approaches include implementing the plaquettes when the Gauss law is added as a constraint, and the primitive Hamiltonian, as explained earlier in this work, is chosen propely \cite{zohar_confinement_2011,zohar_simulating_2012}. Other types of approaches include the motion of virtual particles, that cannot move physically, around a plaquette, carrying with them the $U$ fluxes around a plaquette and closing the trace. This is useful (but gives rise to weak interactions) in the symmetry mapping approach \cite{zohar_quantum_2013}. Another approach based on the effective motion of particles closing a plaquette was recently introduce \cite{homeier_Z2_2020}.

On the stroboscopic or digital side, one may used trotterised time evolution to build the plaquette interactions sequentially, as was shown first for pure gauge models, both Abelian and non-Abelian \cite{tagliacozzo_optical_2013,tagliacozzo_simulation_2012}. Such a stroboscopic scheme, in which the time evolution is trotterised and the plaquette interaction is generated through sequences of two-body interactions with ancillary degrees of freedom, and matter may be simulated as well, was introduced in \cite{zohar_digital_2017,zohar_digital_2017-1}, based on objects called stators \cite{zohar_half_2017}. One of the advantages of this scheme is that the stroboscopic evolution does not affect the gauge symmetry and it is completely protected \cite{zohar_digital_2017-1,bender_gauge_2020}.

Another way to deal with the plaquette interactions is to simply avoid them by switching to the dual picture, when available. There, the magnetic Hamiltonian becomes local, and the electric Hamiltonian becomes interacting - and only with two-body interactions \cite{drell_quantum_1979,kaplan_gauss_2020}. This can be very useful for quantum simulation of pure gauge theories \cite{celi_emerging_2020}, but when dynamical matter is introduced \cite{bender_gauge_2020,haase_resource_2020,paulson_towards_2020}, other parts of the Hamiltonian become complicated and non-local, but tradeoffs have always been and will most likely always be central to quantum simulation.

\section{Summary}

We have reviewed the challenges faced by the quantum simulation of LGTs in more than one space dimension, from a theoretical point of view, which can be summarizes in the following list of requirements (which have been discussed throughout the paper, including ways to bypass some of them):

\begin{enumerate}
	\item \textbf{Quantum simulators of LGTs with fermionic matter in more than $1+1d$ must allow for a way to describe the fermionic statistics.} This can be done by using cold atoms, offering both bosonic and fermionic degrees of freedom with tunable interactions; or by mapping the fermions unitarily and locally to hard-core bosons, which is possible in the presence of a gauge field.
	\item \textbf{In quantum simulators of LGTs  in more than $1+1d$ the gauge field cannot be eliminated, and one must deal with gauge invariance.} This can be done either by imposing gauge invariance on a quantum simulator including both gauge field and matter degrees of freedom (and we have discussed several ways of doing that); by switching, in some cases, to a dual formulation where the redundancy rising from the gauge symmetry is lifted; or, in some cases, by eliminating the matter fields and dealing with a theory including only gauge fields, but with no gauge symmetry. Since the gauge field must be present, one also needs, in some cases, to truncate its local Hilbert spaces, which we have discussed as well.
	\item \textbf{Quantum simulators of LGTs  in more than $1+1d$ have to implement the complicated four-body plaquette interactions.} While such interactions are not "naturally available" in the currently known quantum platforms, we have discussed several ways to obtain them. They can also be avoided when dual formulations are used.
\end{enumerate}

These are special properties of LGTs which cannot be avoided, in general, in more than one space dimension, and have to be taken into consideration when quantum simulators of LGTs in higher dimensions are designed. Since breaking the "bottleneck" of one dimensional simulation is essential from the physical point of view, these questions must be addressed experimentally and revisited theoretically (aiming at further, perhaps more feasible solutions) in the near future.

\section*{Acknowledgement}
This research was supported by the Israel Science Foundation (grant No. 523/20).

\bibliographystyle{ieeetr}

redpajama_set_name: RedPajamaArXiv


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text:
D'Orsi Seniors Bowl – drużynowe mistrzostwa świata seniorów w brydżu sportowym. Seniors Bowl został dodany przez Światową Organizację Brydża jako oficjalne mistrzostwa świata seniorów w roku 2001.

W obecnym formacie (2011) Seniors Cup w mistrzostwach świata spotyka się 22 najlepszych drużyn z całego świata, w których każdy z zawodników musi mieć 60 lat. W pierwszej fazie odbywają się mecze każdy z każdym, a do drugiej fazy, ćwierćfinałów, przechodzi osiem drużyn i rozpoczynają się rozgrywki metodą pucharową (przegrywający odpada).

Zwycięzcy i miejsca drużyny polskiej

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 Mistrzostwa świata teamów open transnational

Przypisy

Linki zewnętrzne
 Oficjalna strona Mistrzostw Świata Teamów (po angielsku)

Drużynowe mistrzostwa świata teamów w brydżu sportowym
Mistrzostwa świata w sporcie

redpajama_set_name: RedPajamaWikipedia


BGO - Flesland Airport (BGO) 7.6 miles from Bergen, NO.
SRP - Stord Airport (SRP) 38.5 miles from Bergen, NO.
There are 2 airports in Bergen. Flesland Airport (BGO) is Bergen's primary airport with at least domestic flights and international flights departing from its runways every week. As of today, airlines operate out of Flesland Airport (BGO). Flesland Airport (BGO) is 7.6 miles from Bergen and offers nonstop flights to cities. Bergen's secondary airport Stord Airport (SRP) is 38.5 miles from Bergen and has airlines operating out of it and offers nonstop flights to cities with at least domestic flights and international flights departing each week.