Origins of Higgs Physics It’s good to talk to each other Symmetry and quantum mechanics • Schrodinger and Weyl • QM=“Applied Group Theory”—operators are generators of symmetries: p=ħ/i d/dx ; H=iħd/dt, etc. (continuous symmetries –not discrete) • Weyl: gauge principle: gauge field=phase of Ψ. Interactions from symmetry! (making local from global, in spirit of GR) • Symmetry=conservation=interaction Broken Symmetry in Condensed Matter • Thermal Phase Transitions: Landau-Tisza Formalism. Quantum theory: Einstein, Debye • Dynamical Role: Bogoliubov, PWA, “Goldstone“ Bosons, rigidity(P R 86,694) • CENTRAL role in interpretation of QM—no BS, no classical physics (No slits, no clocks) How classical physics arises from quantum! • BCS! 46 years late, PR 108, 1175(1957) Broken symmetry in QFT? • The BCS “gauge problem”, 1958 : race to solution (Nambu, Bogoliubov and Shirkov, PWA)—(interlude with KGB) • The Solution: Phys Rev 112, 1900, ‘58 (PWA) The gap is empty! (EXPERIMENT AGREES)-Goldstone bosonsthird component of plasmon; lowest collective mode=Higgson to be (explain later) • 1960 Nambu & Jona-Lasinio from BCS: gap = mass of nucleon, pion = Goldstone boson: mass from interactions massl ess Fermi ons holes gap p electrons superconductivity p gap = mass-Nambu More broken symm in qft: 1962 and after Consequence for BCS: Superconductors have no condensate: no”all-pervading field”--e g coupling to sound vanishes as q0. Sondhi, Oganesyan, Hansson 2004--B-F theory, a “topological order parameter”. And phase transition at Tc is “x-y” type, occurs by proliferation of vortices in vortex liquid, which is observed in cuprates. In ‘62 I began to hear rumors in Cambridge that “Goldstone” bosons were blocking progress with BS theories in QFT. (students, R Eden) returned to Bell summer ‘62 (busy time: Josephson, flux flow & creep, phonon bumps) & talked to J G Taylor (visiting John Klauder) Plasmons, Gauge Invariance and Mass: PR 130, 439 (1962) • 2 gifts from John Taylor: a) it was a problem; b) mysterious paper by Schwinger(PR125,397) that didn’t mention broken symmetry but did say a gauge field need have no zero-mass photon. • So my paper starts out as mysterious as Schwinger, but ends up saying you CAN make mass a la Nambu, but your Goldstone boson disappears into the massive vector boson which results. • Neither I, nor Higgs, nor any of the other 5, actually mentioned the scalar Higgs in those first papers. We invented the W and Z, not the Higgs. The Higgs IS an “Anderson-Bogoliubov” mode in the superconductor. Some Further Comments and Developments 1 Mass for the Higgson appeared first, as far as I can see, in Higgs’ 66 paper where he gave it mass (a la Mexican hat) by fiat. But it seems the “Mexican Hat” is a figment, an imaginary construct?! 2 I gave a lot of thought to observing the Higgs condensate. I was right in that I could see no way of doing so—it has no local meaning!—Is this relevant to the missing zero-point energy-which is why I gave up? 3 But of course—one observes the Higgs” field” by its effect of giving mass to everyone—just as the superconducting gap gaps the whole Fermi surface! I missed this, but should have seen it. 4 Littlewood & Varma (PR B26, 4883, 1982) found a Raman-active AB mode in NbSe2, which can be interpreted as Higgs-like. AB modes play a big role in He-3 (Leggett) but are NOT gapped there. A very modern Problem in CMT Two classes of superfluids I: the liquid Heliums, 3&4: They have condensates, genuine local order parameters II: superconductors, the Higgs. No local OP, only topological. So--which is supersolid He4? (Yes, Virginia, it does really exist). There is strong evidence that the transition Tc is into a vortex liquid, not a normal state. Cold atom experiments on “Bose-Hubbard” model are suggestive-next slide. spielman et al, PRL 105, 110401, 2010 So while we wait with bated breath for new results on the Higgs, we can also expect surprises in ultracold physics--making it clearer than ever that it’s all one subject! Thank you!