# Tagged Questions

Quantum Field Theory (QFT) is the theoretical framework describing the quantisation of classical fields which allows a Lorentz-invariant formulation of quantum mechanics. QFT is used both in high energy physics as well as condensed matter physics and closely related to statistical field theory. Use ...

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### A No-Nonsense Introduction to Quantum Field Theory

I found Sean Carroll's "A No Nonsense Introduction to General Relativity" (about page here. pdf here), a 24-page overview of the topic, very helpful for beginning study. It all got me over the hump ...
1answer
73 views

### Plane waves in QFT

Suppose we work in the metric $(-1,+1)$. How do we describe an incoming particle with a plane wave; $\exp(-\mathrm ikx)$ or $\exp(+\mathrm ikx)$? What's the difference? Does it change if we work in ...
1answer
188 views

### 't Hooft limit of coupling fundamental fermions to Chern-Simons theory

This question is in reference to this paper: arXiv:1110.4386 [hep-th]. I would like to know what is the derivation or a reference to the proof of their crucial equation 2.3 (page 12). In their ...
2answers
159 views

### Why is fractional statistics and non-Abelian common for fractional charges?

Why non integer spins obey Fermi statistics? Why is fractional statistics and non-Abelian common for fractional charges?
0answers
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### integrated vertex operators" in 1-loop open/closed bosonic string amplitude

This question is in reference to the first ~15 minutes of this String Theory lecture by Prof.Shiraz Minwalla, http://theory.tifr.res.in/Videos/strings28_24sep08.mp4 Can one give a reference ...
0answers
46 views

### A particlar normal ordering problem

Say we have an expression of the form: $$\left<0\right|:\phi(x)^2: : \phi(y)^2:\left|0\right>,$$ where $\phi$ is some scalar field. I have heard the claim several times, that in evaluating ...
1answer
75 views

### Higher order covariant Lagrangian

I'm in search of examples of Lagrangian, which are at least second order in the derivatives and are covariant, preferable for field theories. Up to now I could only find first-order (such at ...
0answers
199 views

### Anomalous target space diffeomorphisms for one-loop world-line integrals

The Schwinger effect can be calculated in the world-line formalism by coupling the particle to the target space potential $A$. My question relates to how this calculation might extend to computing ...
1answer
100 views

### Questions about angular momentum and 3-dimensional(3D) space?

Q1: As we know, in classical mechanics(CM), according to Noether's theorem, there is always one conserved quantity corresponding to one particular symmetry. Now consider a classical system in a $n$ ...
2answers
277 views

### Wilson/Polyakov loops in Weinberg's QFT books

I wanted to know if the discussion on Wilson loops and Polyakov loops (and their relationship to confinement and asymptotic freedom) is present in the three volumes of Weinberg's QFT books but in some ...
1answer
294 views

### Perturbative solution + Nonperturbative solution = Full solution?

I am having this silly confusion! Suppose I have a system (a Hamiltonian or an action say) and also suppose I have a perturbation parameter present (say only one in sight) in there, using which I can ...
3answers
270 views

### Could all strings be one single string which weaves the fabric of the universe?

This question popped out of another discussion, about if the photon needs a receiver to exist. Can a photon get emitted without a receiver? A universe containing only one electron was hypothetically ...
1answer
177 views

### Using the covariant derivative to find force between 't Hooft-Polyakov magnetic monopoles

I am reading this research paper authored by NS Manton on the Force between 't Hooft-Polyakov monopoles. I have a doubt in equation 3.6 and 3.7. We assume the gauge field for a slowly accelerating ...
1answer
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### What is the math showing that the time reversed version of an electron is a positron? (+general time reversal question)

As in Wheeler's One Electron Universe idea, how do you show that electrons and positrons are time-reversed versions of each other? Do you just apply time reversal to an electron and out pops a ...
2answers
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### Hawking radiation and black hole entropy

Is black hole entropy, computed by means of quantum field theory on curved spacetime, the entropy of matter degrees of freedom i.e. non-gravitational dofs? What is one actually counting?
1answer
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### Other Gross-Neveu like theories?

By "Gross-Neveu like" I mean non-supersymmetric QFTs whose partition function/beta-function (or any n-point function) is somehow exactly solvable in the large $N_c$ or $N_f$ or 't Hooft limit. ...
2answers
203 views

### Definition of Casimir operator and its properties

I'm not sure which is the exact definition of a Casimir operator. In some texts it is defined as the product of generators of the form: $$X^2=\sum X_iX^i$$ But in other parts it is defined as an ...
3answers
549 views

### Is contextuality required in quantum mechanics?

I still don't really understand what contextuality means in reference to quantum mechanics. If someone could give a clear definition that would be great. It sounds like it means you can't always ...
1answer
74 views

### QED photon propagator to one-loop order gets different answers

I'm a self-studying 14-year-old who has a passion for particle physics. I'm currently trying to calculate the QED photon propagator to one loop. However, in all the places I've looked, even with the ...
2answers
351 views

### Lorentz transformations in Dirac equation

Let's denote a spinor $\xi$. If $(\theta ,\phi)$ are the parameters of a rotation and pure Lorentz transformation, then how $\xi$ could be written as \xi ~\rightarrow~ \exp\left(\ i ...
2answers
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### Independent systems and Lagrangians

Definition 1: The notion of independent systems has a precise meaning in probabilities. It states that the (joint) probability or finding the system ($S_1S_2$) in the configuration ($C_1C_2$) is ...
3answers
86 views

### Bound State of Only Massless Particles? Follows a Time-Like Trajectory?

Is there any way in which a bound state could consist only of massless particles? If yes, would this "atom" of massless particles travel on a light-like trajectory, or would the interaction energy ...
1answer
49 views

### Casimir force using Pauli-Villars regularization

In Zee's Quantum field theory in a nutshell, 2nd edition, p. 74 he claims that:  \sum_a c_a \Lambda_a \sum_n \frac{\omega_n}{\omega_n + \Lambda_a} = - \sum_a c_a \Lambda_a \sum_n ...
1answer
282 views

### Why the pion does not get mass under Spontaneus breaking of chiral symmetry, but the quarks do?

Some sources state that when the mass of a quark goes to zero, it allows for Spontaneous Breaking of Chiral Symmetry and gets a constituent mass of about $200\, \mathrm{MeV}$. Other sources state ...
1answer
86 views

### Different representations of the Lorentz algebra

I've found many definitions of Lorentz generators that satisfy the Lorentz algebra: ...
1answer
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### Chiral anomaly and decay of the pion

I am told that if all classical symmetries were reflected as quantum symmetries, the decay of the neutral pion $$\pi^0 ~\longrightarrow~ \gamma\gamma$$ would not happen. Why would the conservation of ...
2answers
146 views

### How can a pion have a mass, given it's a “field mediator” and created/destroyed continuously?

Maybe some of my assumptions here are basically wrong, but isn't it true that pion is the "mediator" for the strong force field. the quantum field theory basically says that there are no fields, ...
0answers
22 views

### Holomorphic coupling as a source for gaugino condensation

On the top of page 23 of hep-th/03061119, it is pointed out that treating the holomorphic gauge coupling $\tau$ as a background (spurion) superfield allows one to think of its $F$-term, $F_\tau$ as ...
1answer
145 views

### Correlated three-particle Green Function

I know the relationship between normal and correlated two-particle Green Functions for fermions: $$G_c(1,2,3,4)=\Gamma(1,2,3,4)=G(1,2,3,4)+G(1,3)G(2,4)-G(1,4)G(2,3)$$ Also known as irreducible ...
1answer
54 views

### Difference between vector and pseudo-scalar

In physics, a pseudo-scalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion such as improper rotations while a true scalar does not. Can someone show me ...
1answer
260 views

### From quantization under external classical gauge field to a fully quantized theory

Let me take QED for example to clarify my question: The textbook-approach(at least for Peskin&Schroeder) to quantize ED is to first quantize EM field and Dirac field as free fields respectively, ...
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### infrared free QED and Higgsless standard model phenomenology

This is one of those "what if" fantasy world type questions. I like hard sci-fi so please no "well, you changed one thing about the world so now anything goes." :) What if the Higgs had no vev? That ...
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### How many particles are created in the strong electromagnetic field?

Consider a vacuum of charged massless scalar field. Then the uniform and isotropic electric field $E$ is turned on for a time interval $\tau$. The question is, how many scalar particles are created? ...
3answers
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### Problem involving Dirac's equation

I'm stuck in an equation derivation of Ryder's QFT book. Starting with Dirac's equation: $$(i\gamma^\mu\partial_\mu-m)\psi=0$$ If I multiply by $i\gamma^\nu\partial_\nu$, I get: ...
0answers
83 views

### $U(N)$ gauged quantum mechanics

I'm studying the $U(N)$ gauge theory theory in 0+1 dimensions. The aim is to show that this is equivalent to a matrix model. Is there any literature on this topic? The action I am interested in is ...
1answer
209 views

### Wick Rotation, interpretation of $\bar{p}^2$ vs the usual $p^2=m^2$

Suppose we use the metric $(+,-,-,-)$ thus the momentum squared is $p^2 = p_0^2-\vec{p}^2 = m^2>0$ Defining $p_E:=\mathrm{i}\cdot p_0$ and $\bar{p}:=(\,p_E,\vec{p})$ with Euclidean norm ...
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### Derrick’s theorem(2)

Related post : Derrick’s theorem Consider a theory in D spatial dimensions involving one or more scalar fields $\phi_a$, with a Lagrangian density of the form L= \frac{1}{2} G_{ab}(\phi) ...
0answers
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### graph plotting for a solition function [closed]

I have got a solition equation $$\phi(x)= v\tanh\left[ \frac{m}{\sqrt 2} (x-x_0)\right]$$ where, $$m=v\sqrt\lambda$$ Now I need to visualize or simulate this function. I know little about ...
1answer
86 views

### physical importance of regularization in QFT?

The standard lore in QFT is that one must work with renormalised fields, mass, interaction etc. So we must work with "physical" or renormalised quantities and all our ignorance with respect to its ...
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52 views

### Mass of classical kink [closed]

related post Solving the soliton equation without energy The energy density of kink solution is $$\epsilon(x)= \frac{1}{2}(\frac{d \phi}{dx})^2+ V(\phi)$$ where the potential V(\phi)= ...
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50 views

### Standard Quantum Mechanics representation as a constrained 2 + 1 space-time (membrane) theory?

Could a particular Standard Quantum Mechanics representation be a constrained 2 + 1 space-time theory (membrane theory) ? (i) This question is motivated by a possible (approximative) analogy with ...
1answer
208 views

### How do I quantize a classical field theory

I have not been able to find any information about this on the Internet. I am a middle-schooler, 14, who self-studies physics, and I know up to and including ODEs, and some of the calculus of ...
1answer
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### Supersymmetry and non-compact $R$-symmetry group?

The $R$-symmetry for $N$ supercharges is $U(N)$. Is it possible to generalize $R$-symmetry [let's take $U(4)$) to be something like $U(2,2)$ (maybe analogous to Wick rotation of $SO(3,1)$ to ...
1answer
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### Vortex in D dimensions soliton

let us consider the two-dimensional configuration shown in Fig. 3.1a. The lengths of the arrows represent the magnitude of φ, while their directions indicate the orientation in the $φ_1 -φ_2$ plane. ...
3answers
60 views

### Valid theory in all dimensions for solitary waves

I'm studying soliton (solitary waves). They are many theory which explain the phenomenon, like sine-Gordon model. But sine-Gordon model has limitations when it applies to 4 dimension because it is ...
2answers
51 views

### Derrick’s theorem

Consider a theory in D spatial dimensions involving one or more scalar fields $\phi_a$, with a Lagrangian density of the form L= \frac{1}{2} G_{ab}(\phi) \partial_\mu \phi_a \partial^\mu \phi_b- ...
1answer
34 views

### Creating a state of definite momentum and position(within uncertainty limit)

claim: $a^{\dagger}$= $\int d^{3}kf_{1}(k)a^{\dagger}(k)$ Creates a state with Localized momentum $k_{1}$and localized position near origin; where $f_{1}(k)$ \$\propto ...
1answer
83 views

### sine-Gordon equation

I have derived a solition equation (2 dimensions) from scalar field theory $$\varphi(x) = v\tanh\Bigl(\tfrac{1}{2}m(x - x_0)\Bigr),\tag{1}$$ and also I have got sine-Gordon equation for solition ...
1answer
206 views

### Crazy Dirac Deltas

I'm not expecting any rigor in the following and the answers...since we're dealing with Dirac deltas in the context of QFT. Consider the integral  \int d^4q\ \Theta(q_0)\Theta(p_{3,0}+q_0)\ ...
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### Emergent symmetries

As we know, spontaneous symmetry breaking(SSB) is a very important concept in physics. Loosely speaking, zero temprature SSB says that the Hamiltonian of a quantum system has some symmetry, but the ...
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