Modified Formulations of QED  

Various Approaches > s.a. modified electrodynamics [including in media]; QED; Stochastic Electrodynamics; topological field theories.
* Scalar electrodynamics: A well-known version is the Pauli-Weisskopf theory, but Majorana had developed an earlier theory.
* Pseudo Quantum Electrodynamics (PQED): A generalization containing the pseudodifferential operator \(\square\)1/2; It plays an important role in the description of electromagnetic interactions of charged particles confined to a plane, such as in graphene or in hetero-junctions displaying the quantum Hall effect.
@ Without second quantization: Barut et al PRA(88), Barut & Dowling PRA(89) [electron g – 2], PRA(90) [2-level atom]; Barut PS(88) [rev]; Morgan a0908 [empirically equivalent random field]; Louis-Martinez MPLA(12)-a1107 [derivation of the Breit equation]; Huang & Batelaan a1206 [Random Electrodynamics coupled to a classical harmonic oscillator]; Cetto et al a1301 [atomic radiative corrections from the zero-point radiation field]; Bennett AP(14)-a1406 [parametrized Dirac wave equation]; > s.a. energy [self-energy]; photons [against photons as physical objects].
@ Massive / with photon mass: Esposito FP(02); Schroer EPJC(15)-a1504; Belokogne & Folacci PRD(16)-a1512 [Stückelberg electromagnetism in curved spacetime]; > s.a. photon.
@ Supersymmetric: Herzog & Klose NPB(10)-a0912 [atom-like bound states].
@ World-line methods: Dittrich & Shaisultanov PRD(00)ht [vacuum polarization].
@ Without photons: Hainzl & Siedentop CMP(03) [mass and charge renormalization]; Hainzl et al ARMA(09)mp/06, Sok a1407 [mean-field approximation].
@ With higher derivatives: Podolsky & Kikuchi PR(44) [Podolsky's electrodynamics]; Accioly & Scatena MPLA(10) [limits on the coupling constant].
@ Non-local electrodynamics: Chrétien & Peierls PRS(54); Scharnhorst PRS(95) [gauge]; Mei a0902; Marino et al PRD(14)-a1408 [theories with fractional powers of the d'Alembertian operator]; Modesto et al PRD(15)-a1506 [finite theory]; Donoghue & El-Menoufi a1507 [and the curvature expansion].
@ Scalar electrodynamics: Guendelman et al PLB(95)ht [and volume-preserving diffeomorphisms]; Shvedov ht/04 [Hamiltonian, semiclassical]; Esposito AdP(07)-a0710 [Majorana's theory]; Bufalo & Pimentel PRD(13)-a1404 [BFV quantization]; > s.a. modified electrodynamics.
@ Non-linear theory: Azatov & Chkareuli PRD(06) [and Lorentz invariance]; Chkareuli & Kepuladze PLB(06) [massive, and Lorentz invariance]; Shabad & Usov PRD(11)-a1101 [causality and unitarity]; Plimak & Stenholm a1104 [phase-space techniques].
@ PT-symmetric: Milton CzJP(03)ht, CzJP(04)ht/03; Ford JPA(08)-a0807 [non-Hermitian, magnetic]; Milton et al PTRS(13)-a1204 [and unitarity].
@ With Lorentz symmetry violation: Ferrari et al GRG(17) [and torsional gravity, singular spinor fields]; > s.a. lorentz-violating theories.
@ With varying fine-structure constant: Ferrero & Altschul PRD(09)-a0910 [Lorentz and gauge symmetry violation].
@ Approaches to quantization: Bufalo et al PRD(11)-a1008 [path integral quantization]; Francis EJTP(13)-gq/06 [using a finite-dimensional Hilbert space]; Zarei et al IJTP(11) [Krein-space quantization]; Marrocco a1504 [quantization using only classical concepts].
@ Other fields or variables: Kijowski et al LMP(95) [in terms of gauge-invariant quantities]; Savvidy a1005, a1111 [spin-3/2 field]; Akhmeteli EPJC(13)-a1108 [based on spinor electrodynamics]; Naudts a1506 [2D quantum harmonic oscillators].
@ Other approaches: Oakley PS(90); Scharf 95 [causal]; Bender & Milton ht/98; Ribarič & Šušteršič ht/99; Razmi & Abbassi qp/99; Brana NCB(01) [without divergent self-interaction]; Smith & Raymer NJP(07); Majumdar & Bhattacharjee a0904 [gauge-free]; Rivera & Schuller PRD(11) [general linear electrodynamics]; Sigal a1110-ln [non-relativistic, theory of radiation]; Kowar a1111 [non-instant field model]; Bufalo et al PRD(12)-a1212, IJMPA(17)-a1510 [renormalizability, causal approach]; Schreck PRD(14)-a1311 [based on birefringent modified Maxwell theory]; Drummond PRD(17)-a1603 [bimetric QED, and Lorentz violation]; Naudts a1801 [transverse photons for Coulomb force].
> Related topics: see boundaries [euclidean]; Lee-Wick Electrodynamics; non-commutative gauge theory; photon [wave function]; Proca Theory; QED in curved spacetimes [including (quantum) gravity effects].

Schwinger Model > s.a. entanglement entropy.
* Idea: A theory of 2D massless QED.
@ References: Melnikov & Weinstein PRD(00)hl [lattice]; Avossevou & Govaerts ht/02-proc [non-perturbative, gauge-invariant quantization]; Muslih MPLA(03) [chiral, path-integral quantization]; Bracken IJMPA(08)-a0710 [chiral, constraints and quantization]; Belvedere et al JPA(11)-a0908 [at finite temperature].
@ On general manifolds: Azakov IJMPA(06)ht/05 [on S1, path integral vs canonical]; Stuart a1206 [on S1, regularization and gauge invariance]; Harder & DeLillo a1405 [in curved spacetime].

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