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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