Modified Versions of Electromagnetism  

Altenative Formulations > s.a. kaluza-klein; modified QED; photon [including massive]; regge calculus [discrete].
* Feynman's approach: Derive Maxwell's theory from quantum mechanics.
* Lanczos' approach: A biquaternionic field theory in which point singularities are interpreted as electrons.
* Pre-metric: The precursor was Einstein's proof in 1916 that electromagnetism can be put in generally covariant form; Developed with constributions by Kottler, Cartan, van Dantzig, Schouten & Dorgelo, Toupin & Truesdell, and Post; More recently, motivated by the 1962 suggestion by A Peres that electromagnetism is fundamental and gab a subsidiary field.
@ Gauge-invariant: Kijowski & Rudolph LMP(93) [spinor electrodynamics]; Przeszowski JPA(05)ht [light-front variables].
@ Feynman's approach: Dyson AJP(90) and comments; Lee PLA(90), comment Farquhar PLA(90); Tanimura AP(92); Kauffman & Noyes PRS(96); Montesinos & Pérez-Lorenzana IJTP(99)qp/98; Paschke mp/03 [on curved spaces]; Cariñena & Figueroa JPA(06)ht, Kauffman IJTP(06) [and non-commutativity].
@ Accelerated frames: Muench et al PLA(00)gq, Mashhoon AdP(03)ht, PRA(04), PLA(07)ht [non-local]; Hauck & Mashhoon AdP(03)gq [waves in rotating frame]; Mashhoon PRA(05)ht [rotating, non-local].
@ Pre-metric: Gross & Rubilar PLA(01) [and spacetime metric]; Rubilar AdP(02)-a0706 [emergence of light cone]; Kaiser JPA(04)mp [pa conservation]; Itin & Hehl AP(04)gq [and spacetime signature]; Hehl & Obukhov PLA(04)phy, FP(05)phy/04; Lämmerzahl & Hehl PRD(04)gq; Delphenich gq/04 [and complex geometry], AdP(05), gq/05-in [symmetries], gq/05-in [and spinors]; Hehl & Obukhov GRG(05) [history, dimensions, units]; Itin PRD(05)ht [vacuum no-birefringence conditions], JPA(07) [photon propagator].
@ Lanczos approach: Lanczos (19)phy/04, ZfP(29)phy/05, PZ(30)phy/05; Gsponer & Hurni in(98)mp/04, FP(05)mp/04; > s.a. em in curved spacetime [Lanczos-Newman].
@ Geometric formulation: Tonti in(95); Olkhov ht/02, ht/02-in; Poplawski a0802 [unified with gravity]; > s.a. particles [models].
@ Manifestly covariant: Hillion NCB(99); Marmo & Tulczyjew a0708 [and introduction of particles].
@ Other formulations: Harmuth et al 01 [magnetic dipole currents??]; Kravchenko mp/02-in, Jack mp/03 [quaternionic]; Coll AFLB(04)gq/03; Bzdak & Hadasz PLB(04) [and sqrt of Dirac]; Gottlieb mp/04; Holland PRS(05)qp/04 [Eulerian hydrodynamic model]; Rahman phy/04-in [ito two 2-component relativistic fluid]; De Montigny & Rousseaux EJP(06)phy/05 [non-relativistic limits]; Pierseaux & Rousseaux phy/06; Gogberashvili JPA(06)ht/05, Tolan et al NCB(06) [octonionic]; De Nicola & Tulczyjew a0704 [variational, ito de Rham even and odd forms]; > s.a. Clebsch Potential.

Non-Linear > s.a. born-infeld; duality; singularities; Smarr Formula.
* Motivation: Arises as an effective theory when one takes into account QED effects; > s.a. effective quantum field theory.
@ General references: Gibbons & Rasheed PLB(96) [+ axion + dilaton]; Sowa JGP(03); Duplij et al a0711-in [supersymmetric].
@ And cosmology: De Lorenci et al PRD(02) [non-singular FRW]; García-Salcedo & Bretón CQG(03), CQG(05)gq/04 [singularity-free Bianchi]; Camara et al PRD(04)ap [FRW]; Novello et al CQG(07)gq/06; Kunze a0710 [primordial magnetic fields]; > s.a. acceleration.
@ Other phenomenology: Cooperstock FPL(89) [+ scalar, and particle models]; De Lorenci et al PLB(00), Visser et al gq/02-in [birefringence]; Burinskii & Hildebrandt PRD(02) [particle-like solutions]; Obukhov & Rubilar PRD(02)gq [waves]; Gaete & Schmidt IJMPA(04)ht/03 [Coulomb]; Mosquera & Salim ApJ(04)ap/03 [and neutron star redshift]; Delphenich ht/03 [and QED]; Mbelek & Mosquera a0707 [and variation of fine structure constant]; Mosquera et al a0710 [and cosmological redshift]; > s.a. anomalous acceleration, Gravastar.

Other Theories > s.a. black holes; BRST; Coulomb's Law; curved spacetime; history; non-commutative fields; Proca; Supermanifolds.
* 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.
* Stochastic electrodynamics: 2005, Developed over the past few decades, with a view to establishing it as the foundation for quantum mechanics; The theory had several successes, but failed when applied to the study of particles subject to non-linear forces; An analysis of the failure showed that this was due to the methods used to construct the theory, particularly the use of a Fokker-Planck approximation and perturbation theory; A new, non-perturbative approach has now been developed, called linear stochastic electrodynamics.
* Ritz theory of electrodynamics: (1908–1911) 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.
@ Stochastic electrodynamics: Boyer PRD(75), PRD(75); Boyer PRD(80) [and acceleration radiation]; Claverie et al PLA(80), Claverie & Soto JMP(82) [H atom]; de la Peña-Auerbach & Cetto pr(84); de la Peña & Cetto 96; Cole & Zou qp/03 [and H ground state]; de la Peña & Cetto qp/05 [and quantum mechanics], FP(06); > s.a. hidden variables [tests], quantum oscillators.
@ Scalar: Kruglov AFLdB(01)mp [s = 0, 1]; Kajantie et al NPB(04) [duality and scaling]; Esposito a0710-AdP [Majorana's theory].
@ Ritz theory: Ritz ACP(08)tr; in Jackson 75; comments by Fritzius web(98).
@ Quantum-gravity-motivated, Lorentz-violating: Lämmerzahl et al PRD(05) [and charge non-conservation]; Montemayor & Urrutia PLB(05) [synchrotron radiation in Myers-Pospelov]; Dvali et al PRL(05)ht [instantaneous at large d]; Altschul PRD(07)ht [Cerenkov radiation]; Montemayor & Urrutia GRG(07) [phenomenology]; > s.a. modified lorentz symmetry.
@ Non-gauge-invariant: van Oosten EPJD(00)phy/01 [based on Fermi Lagrangian]; Rousseaux AFLdB(03).
@ Massive, Lorentz electrodynamics: Appel & Kiessling AP(01)mp/00.
@ 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: Dvoeglazov Ap(98)phy [rev]; Antoci GRG(91)gq/01 [Einstein's unified theory]; Hehl et al IJMPA(02)gq-in [generally covariant]; Martinez-Ledesma & Mendoza RMF(04)ap/02 [varying ]; Kiessling JSP(04)mp/03, JSP(04)mp/03; Donev & Tashkova ht/04 [extended]; Rousseaux EPL(05)phy [Galilean electromagnetism]; Mitskievich a0707-in [higher dimensions]; > s.a. gauge theory, monopole [Alice electrodynamics].
> Related topics: see causality [action at a distance, non-local]; chern-simons; clifford algebra; quantum gravity phenomenology; spinors in field theory; unification.

Semiclassical, with Quantum Fields > s.a. aharonov-bohm; charge [quantization]; quantum dirac fields; spacetime foam.
@ And spinors: Laporte & Uhlenbeck PR(31); Kijowski & Rudolph LMP(93); Olkhov qp/01-in.
@ Semiclassical particle in classical field: Bordovitsyn & Myagkii mp/01 [electron in B field].

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