QED – Quantum Electrodynamics  

In General > s.a. Electrodynamics; electromagnetism / QED phenomenology [including media and background fields].
* Idea: The theory of the coupled, quantized Maxwell theory for the (vector) electromagnetic field coupled to (Dirac spinor) electron fields.
* 1948: Schwinger solves the problems of renormalization in QED, followed by the work of Feynman and Tomonaga.
* 1952: Dyson's arguments suggest that the perturbation series in quantum electrodynamics cannot be convergent but are asymptotic.
* 1955: Landau's argument that the effective running coupling constant has a pole (Landau singularity) at some very high energy scale.
* Status: It is the most accurate theory we have, and gives extremely precise predictions; However, because its perturbation series diverge (they are asymptotic series) and of the Landau pole problem, it is considered as an effective low-energy theory, valid up to some cutoff energy.

Canonical Approach > s.a. fock space; geometric quantization; Wavelets.
* Approaches: It can be carried out in a fixed gauge, or à la Dirac.
@ General references: Dirac PR(65) [Heisenberg representation]; Arthurs PLA(79) [in terms of E and B]; Löffelholz et al JMP(03) [Gauss law and existence of propagator]; Frolov a1403 [formulations]; Blasone et al JPCS(18)-a1801 [and the emergence of gauge invariance].
@ Loop representation: Ashtekar & Rovelli CQG(92); Ashtekar et al JGP(92) [self-dual representation]; Brügmann LNP(04)gq/93; Leal MPLA(96)ht; Ashtekar & Corichi CQG(97)gq/96; Corichi & Krasnov MPLA(98)ht/97; Varadarajan PRD(00)gq [Fock space]; Carrión-Álvarez PhD(04)mp [unsmeared Wilson loops and Fock space]; Leal MPLA(10)-a0910 [dual loop representation]; > s.a. monopoles.
@ Flux uncertainty relations: Ashtekar & Corichi PRD(97)ht; Freed et al CMP(07)ht/06, AP(07)ht/06.
@ Special cases: Gambini et al PRD(98)ht/97 [2D compact, loop variables]; Bojowald JMP(00)ht/99 [spherical symmetry, and abelian BF]; Leal & López JMP(06)ht/04 [with magnetic monopole].

Covariant Approach
* Lagrangian: This approach requires adding a gauge-fixing term to the Lagrangian,

\(\cal L\)G = −\(1\over2\)ζ−1 (Aa;a)\(^2\),

with ζ a constant parameter (ζ = 1, Feynman gauge, which actually leads to the Lorenz gauge condition; ζ → 0, Landau gauge); The equation of motion becomes [ηab \(\square\) − (1−ζ−1) ∂a ∂b] Ab = 0 or, in the Feynman gauge; \(\square\) Aa = 0.
* Interpretation: Problems with the number of degrees of freedom can be handled with the Gupta-Bleuler formalism.
@ References: Schwinger PR(48), PR(49); Nambu PTP(50); Misra & Warawdekar PRD(05) [and light-front, 1-loop equivalence].

Other Approaches and Situations > s.a. quantum gauge theories; stochastic quantization; yang-mills theories.
* Path integral: It can be done, but it introduces ghosts in the theory, because of gauge invariance.
@ General references: Thirring & Narnhofer RVMP(92) [covariant without ghosts]; Swanson FP(00) [canonical vs path integral]; Burch JMP(04)qp/03 [histories]; Arbatsky mp/04; Steinmann ht/04-conf [Gupta-Bleuler vs Coulomb gauge formulations]; Yearchuck et al a0909; Ciolli et al RVMP(15)-a1305 [QED as a representation of the net of causal loops in Minkowski spacetime]; Siringo PRD(14) [variational method]; Bennett et al EJP-a1506 [physically motivated].
@ Perturbative: Steinhauser PRP(02) [multi-loop]; Dunne JHEP(04)ht/03 [2-loop, simplification]; Azam ht/04, MPLA(06)hp/05 [series divergence], hp/06-wd [and Landau pole]; Filippov qp/06-conf [new approach]; Sakhnovich a1606, a1710 [new approach to the divergence problems].
@ Non-perturbative: Rochev JPA(00); Ilderton a1901 [on the string-field conjectured breakdown of perturbation theory]; > s.a. algebraic quantum field theory.
@ Discretized, on a lattice: Armand-Ugón & Fort PLB(92) [phase transition]; Kijowski & Thielmann JGP(96); Kijowski et al CMP(97) [observables and superselection]; Ercolessi et al PRD(18)-a1705 [in 1+1 dimensions, simulation]; > s.a. Discrete Models; regge calculus.
@ Related topics: Czachor ht/02, & Syty qp/02 [non-canonical]; Noltingk JMP(02)gq/01 [BRST quantization of histories electrodynamics]; Manoukian & Viriyasrisuwattana IJTP(07) [photon propagation in spacetime]; Karplyuk & Zhmudsky PRD(12)-a1206 [new method for calculating amplitudes].
> Related topics: see feynman propagator; modified formulations [including curved spacetime]; photon [propagator]; string phenomenology.

Theoretical Concepts and Effects > s.a. information theory; locality; modified electrodynamics; photons; renormalization of gauge theories; vacuum.
@ States: Buchholz LNP(82) [state space]; Alekseev & Perina PLA(97) [squeezing, chaos-assisted]; > s.a. Squeezed States.
@ Semiclassical: Sonego pr(91); Stewart JPA(00)-a1606 [not gauge invariant]; Naudts & De Roeck IJTP(04)mp/03 [with classical Aa]; Polonyi PRD(06)ht [crossover field theory], PRD(08)-a0801; Ghose a1705 [interpolating theory between quantum and classical electrodynamics]; > s.a. quantum field theory states.
@ At finite temperature: Elmfors & Skagerstam PLB(95)ht/94; Cervi et al PRD(01), Alfaro et al IJMPA(10)-a0904 [Lorentz and CPT violation]; Andersen PRD(02) [low-T]; Kazakov & Nikitin a0910, EPL(10) [vanishing effective electromagnetic field]; > s.a. effective action.
@ Radiation damping, decoherence: Breuer & Petruccione in(00)qp/02; > s.a. decoherence.
@ Interpretations: Kaloyerou PRP(94) [causal field]; Marshall qp/02 [classical]; Bacelar a1201 [relationship with classical theory]; > s.a. quantum field theory.
@ Non-classical aspects: Klyshko PLA(96); Roy & Roy JPA(97); Paris PLA(01)qp; Li PLA(08) [photon-added thermal state].
@ Gauge issues: Hojman AP(77) [true degrees of freedom in any gauge]; Esposito PRD(97)ht/96 [conformally invariant gauge]; Arnone et al JHEP(05)ht [manifestly gauge-invariant]; Solomon qp/06 [negative energy states in temporal gauge], qp/07 [spacelike energy-momentum vector].
@ Fluxes: Weigel JPA(06)ht [flux tubes]; Rañada & Trueba FP(06) [topological quantization].
@ Related topics: Crone & Sher AJP(91)jan [broken U(1)]; Anastopoulos & Zoupas PRD(98)ht/97 [ρeff for spinors]; Kondo PRD(98)ht [confining phase?]; Ribarič & Šušteršič ht/00 [regularization]; Bagan et al PLB(00)ht [particle description]; Buchholz et al AP(01) [charge delocalization]; Lieb & Loss CMP(04)mp [polarization vectors]; Bordag PRD(04)ht [and boundary conditions]; Alexandre AP(04) [dynamical mass generation in QED3]; Aragão et al PLA(04) [highly peaked phase distribution]; Efimov TMP(04) [stability]; Herdegen APPB(05)ht/04 [asymptotic structure]; Ilderton NPB(06) [recurrence relations between amplitudes]; Marsh a0809 [negative energies]; Fry PRD(11) [stability]; Naudts a1704-conf [emergence of Coulomb forces].
> Other effects: see correlations; duality; emergence; entanglement; geometric phase; Landau Pole; particles and photons in quantum gravity.

References > s.a. history of quantum physics; light; path integrals for field theory; quantum dirac fields; quantum field theory [including pilot-wave].
@ General: Dirac et al PZS(32); Feynman PR(49), PR(50), PR(51), Sci(66)aug; Prokhorov SPU(88); de la Torre EJP(05).
@ Texts, I: Feynman 85.
@ Texts, III: Thirring 58; Feynman 61; Ahiezer & Beresteckii 65; Källén 72; Cohen-Tannoudji et al 92; Milonni 94; Gribov & Nyiri 00; Steinmann 00 [perturbative]; Greiner & Reinhardt 02; Gingrich 06 [numerous exercises]; Grozin 07; Zeidler 09; Aitchison & Hey 12.
@ Sources, reprints: Schwinger ed-58; Miller 94.

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