Modified Versions of Electromagnetism  

Non-Linear Electrodynamics > s.a. born-infeld theory; duality; Smarr Formula; teleparallel gravity.
* Motivation: It arises as an effective theory when one takes into account QED effects, and may also arise from a possible non-minimal coupling to gravity in the classical theory; > s.a. effective quantum field theory.
* Status: 2010, There is no experimental evidence, but high-intensity lasers and strong magnetic fields are expected to lead to more stringent tests.
@ General references: Pisello IJTP(77); Gibbons & Rasheed PLB(96) [+ axion + dilaton]; Sowa JGP(03); Duplij et al JPA(08)-a0711-in [supersymmetric]; Shabad & Usov a0911 [causality principle and convexity of Lagrangian]; Donev & Tashkova a1305 [based on an extended Lie derivative]; Aschieri et al proc(14)-a1310 [and higher-derivative theories, duality]; Gaete & Helayël-Neto EPJC(14)-a1408.
@ SO(2) duality-invariant conformal extension: Bandos et al PRD(20)-a2007; Kosyakov PLB(20)-a2007; Ballon Bordo et al a2011 [Taub-NUT solutions].
@ And FLRW cosmology: De Lorenci et al PRD(02) [non-singular]; Camara et al PRD(04)ap; Vollick PRD(08)-a0807 [and acceleration]; García-Salcedo et al a0905 [with dark matter], PRD(14)-a1312 [spatially flat, issues]; Kruglov IJMPA(17)-a1705 [inflation].
@ Other cosmology: García-Salcedo & Bretón CQG(03), CQG(05)gq/04 [singularity-free Bianchi]; Novello et al CQG(07)gq/06; Kunze PRD(08)-a0710 [primordial magnetic fields]; Benaoum & Ovgun CQG-a2105 [matter-antimatter asymmetry]; > s.a. theories of cosmological acceleration.
@ And particle models: Cooperstock FPL(89) [+ scalar field]; Burinskii & Hildebrandt PRD(02) [particle-like solutions]; Vellozo et al IJTP(09)-a0811 [self-energy and electron charge stability]; Zaslavskii G&C(10)-a1004 [coupled to gravity, Zel'dovich states].
@ Coupled to gravity: Hollenstein & Lobo PRD(08)-a0807 [f(R) gravity]; Díaz-Alonso & Rubiera-García a1001-MG12 [spherical]; Mazharimousavi et al EPJC(14)-a1304 [in 2+1 dimensions]; Dymnikova & Galaktionov CQG(15)-a1510 [rotating electrically charged black holes and solitons]; Chinaglia a1512; Kruglov PRD(16)-a1608 [charged black holes]; > s.a. lovelock gravity.
@ Heisenberg-Euler type electrodynamics: Gaete et al AHEP-a1509 [birefringence]; Kruglov MPLA(17)-a1705 [corrections to Coulomb's law, black holes].
@ Birefringence: De Lorenci et al PLB(00); Visser et al gq/02-fs; de Melo et al MPLA(15)-a1407 [and causal structure]; De Lorenci et al PRD(13)-a1502 [multirefringence phenomena]; Gaete & Helayël-Neto EPL(17)-a1709.
@ Astrophysics and cosmology: Mosquera & Salim ApJ(04)ap/03 [and neutron-star redshift]; Mbelek & Mosquera MNRAS(08)-a0707 [and variation of fine-structure constant]; Mosquera et al a0710 [and cosmological redshift]; Corda & Mosquera MPLA(10)-a0905 [and black-hole singularities]; Mosquera & Lambiase PRD(09) [primordial magnetic fields and gravitational baryogenesis]; Kruglov IJMPA(17)-a1710 [new model, and black holes]; Samanta et al PRD-a1810 [singularities and accelerated expansion].
@ Other phenomenology: Obukhov & Rubilar PRD(02)gq [wave propagation]; Gaete & Schmidt IJMPA(04)ht/03 [Coulomb]; Delphenich ht/03 [and QED]; Goulart de Oliveira & Perez Bergliaffa CQG(09)-a0905 [effective metric]; Mazharimousavi & Halilsoy PLA(11)-a0908 [resolution of historic problem]; Accioly et al IJMPA(10)-a0912 [in an external magnetic field]; Dereli & Tucker EPL(10)-a1001 [tests, framework]; Goulart EPL(16)-a1602 [knotted solutions]; Mazharimousavi & Halilsoy CQG(20)-a2008 [colliding waves]; > s.a. anomalous acceleration; energy [electron self-energy].
> Solutions, coupling to gravity: see Gravastar; kerr-newman black holes; spacetime singularities; spherical solutions in general relativity; Stealth Fields.

Quantum-Gravity-Motivated, Lorentz-Violating Theories blue bullet s.a. quantum-gravity effects on electrodynamics.
* Motivation: Obtain a theory that violates Lorentz symmetry, by introducing a dependence of the speed c of light on the motion of the source, or anisotropy.
@ General references: Lämmerzahl et al PRD(05) [and charge non-conservation]; Dvali et al PRL(05)ht [instantaneous at large d]; Knoll & Yavneh JPA(10)-a0902 [scale-covariant "quantum deformation"]; Casana et al PRD(09)-a0907 [from standard-model extension]; Li et al PLB(09)-a0907 [CPT-violating with Chern-Simons term, and modified gravity]; Romero et al MPLA(10)-a1006 [à la Hořava]; Leonard & Woodard PRD(12)-a1202 [graviton corrections]; Moayedi et al AHEP(13)-a1303, Prudencio et al a1706 [with minimal measurable length].
@ Discretized: Das CJP(10)-a0811 [covariant discrete phase space]; > s.a. regge calculus.
@ Unified theories: Antoci GRG(91)gq/01 [Einstein's unified theory]; > s.a. unification.
@ Phenomenology: Montemayor & Urrutia PLB(05) [synchrotron radiation in Myers-Pospelov]; Altschul PRD(07)ht [Cerenkov radiation]; Montemayor & Urrutia GRG(07); Gubitosi et al JCAP(09)-a0904 [from cmb polarization data].
> Related topics: see kaluza-klein theory; modified lorentz symmetry.

Related Theories > s.a. formulations of maxwell's theory [including pre-metric].
* Ritz theory of electrodynamics: A modification of electromagnetism in which the Maxwell equations involving sources are modified so that the speed of light is c only relative to the source.
* Podolsky theory of electrodynamics: A generalized electrodynamics with higher-order derivatives.
@ General references: Dvoeglazov Ap(98)phy [rev]; Bogolubov & Prykarpatsky UJP(09)-a0909, FP(10) [various theories, and Dirac quantization]; Pfeifer & Siemssen PRD(16)-a1602 [general linear electrodynamics]; Errasti Díez et al PRD(20)-a1905 [general Lagrangian theory].
@ QED corrections: Ni a1109-ch [Parametrized Post-Maxwellian framework, foundations]; Tomazelli & Zanellato IJMPA(13) [vacuum fluctuations].
@ Scalar theory: Kruglov AFLB(01)mp [s = 0, 1]; Kajantie et al NPB(04) [duality and scaling]; Esposito AdP(07)-a0710 [Majorana's theory]; in Akhmeteli JMP(11)-a1008 [real vs complex matter field].
@ Ritz theory: Ritz ACP(08)tr; Ritz & Einstein PZ(09); in Jackson 75; comments and articles by Fritzius web(11).
@ Podolsky theory: Matthews MPCPS(49); Galvão & Pimentel CJP(88) [canonical structure]; Cuzinatto et al IJMPA(11)-a0810 [phenomenology]; Kruglov JPA(10)-a0907 [1st-order formalism and solutions]; Zayats AP(14)-a1306 [self-interaction]; Gratus et al JPA(15)-a1502 [self-force]; Bonin et al a1608 [multipole expansion]; Granado et al EPL(20)-a1912 [from a condensation of topological defects]; Araújo & Maluf BJP(21)-a2003 [photon gas thermodynamics]; > s.a. modified quantum electrodynamics.
@ Wheeler-Feynman theory: Deckert et al a1212 [instructive approximate model].
@ Non-gauge-invariant theory: van Oosten EPJD(00)phy/01 [based on Fermi Lagrangian]; Rousseaux AFLB(03).
@ Massive, Lorentz electrodynamics: Appel & Kiessling AP(01)mp/00; Cafaro & Ali AACA(07)mp [spacetime algebra approach]; > s.a. modified QED.
@ Topological formulations: Delphenich AdP(05)ht/03; Barrett 08.
@ Topologically massive: Accioly & Dias IJMPA(06)ht/05 [and unitarity]; Ghalati et al ht/06 [first-order form, canonical]; > s.a. photon.
@ Other proposals: Assis 94 [Weber's electrodynamics]; Hehl et al IJMPA(02)gq-in [generally covariant]; Martinez-Ledesma & Mendoza RMF(04)ap/02 [varying α]; Kiessling JSP(04)mp/03, JSP(04)mp/03; Donev & Tashkova ht/04 [extended]; Rousseaux EPL(05)phy [Galilean electromagnetism]; Kruglov CJP(08)ht/06; Roscoe a0904 [without scalar potential]; Tarasov AP(08)-a0907 [fractional]; Klinkhamer & Schreck NPB(11)-a1011 [isotropic modified Maxwell theory]; Sheykhi & Hendi IJTP(11)-a1012 [entropic origin and corrections to Coulomb's law]; Kowar a1111 [non-instant field model]; Navarro & Sancho JMP(12)-a1201, Gallego Torromé a1207 [higher-order forms]; Segev a1412 [as a special case of continuum mechanics]; > s.a. finsler geometry and physics; monopoles [Alice electrodynamics].
> Other theories: see Proca Theory; quaternions; spin-1 fields; Stochastic Electrodynamics.
> Related topics: see black holes; BRST; causality [action at a distance, non-local]; chern-simons theory; clifford algebra; Coulomb's Law; electricity [tests]; electromagnetism in curved spacetime [and higher dimensions]; gauge theory; history of physics; modified QED; non-commutative fields; photon [including massive]; plasma physics [Aristotelian electrodynamics]; spinors in field theory; Supermanifolds; torsion in physics; types of symplectic structures [multisymplectic formalism].

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