Formulations of Maxwell's Theory  

In General > s.a. electromagnetism; modified theories of electromagnetism.
* Feynman's approach: Derive Maxwell's theory from quantum mechanics.
* Lanczos' approach: A biquaternionic field theory in which point singularities are interpreted as electrons.
@ Need for potentials: Aharonov et al a1502 [local interactions of gauge-dependent potentials, vs non-local interactions of gauge-invariant quantities]; > s.a. aharonov-bohm effect.
@ Gauge-invariant: Kijowski & Rudolph LMP(93) [spinor electrodynamics]; Przeszowski JPA(05)ht [light-front variables]; Mansfield JHEP(12)-a1108 [electric flux lines].
@ Wheeler-Feynman direct interaction: Wheeler & Feynman RMP(45), RMP(49); De Luca JMP(09) [variational principle]; Bauer et al JSP(14)-a1306; > s.a. causality.
@ Feynman's approach: Dyson AJP(90)mar 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]; Narayana Swami IJTP(09) [and quantum gravity].
@ 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. electromagnetism in curved spacetime [Lanczos-Newman electrodynamics].
@ In 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]; Maluf & Faria a1110-ch; > s.a. Reference Frames.
@ Geometric formulations, and topology: Tonti in(95); Olkhov ht/02, ht/02-proc; Popławski a0802, MPLA(09) [unified with gravity]; Boozer PLA(10) [2D, role of topology]; Myrvold BJPS(11) [holonomy interpretation, implications and non-separability]; Kulyabov et al a1403 [material media and effective spacetime geometry]; Mannheim a1407 [and PT symmetry and conformal symmetry]; Kim & Kim a1507 [5D Kaluza-Klein theory]; > s.a. particles [models]; teleparallelism.
@ Emergent: Wang PRD(10) [entropic origin]; Barceló et al NJP(14)-a1407; > s.a. emergent gravity.

Pre-Metric Formulation > s.a. lines [electromagnetism and line geometry].
* History: The precursor was Einstein's proof in 1916 that electromagnetism can be put in generally covariant form, compatible with general relativity (only the constitutive tensor density depends on the metric); Developed with contributions by Weyl (1918), Murnaghan (1921), Kottler (1922), Cartan (1923), 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.
@ General references: Kaiser JPA(04)mp [pa conservation]; Hehl & Obukhov PLA(04)phy, FP(05)phy/04; Lämmerzahl & Hehl PRD(04)gq; Delphenich gq/04 [and complex geometry], AdP(05), gq/05-conf [symmetries], gq/05-conf [and spinors]; Itin PRD(05)ht [vacuum no-birefringence conditions], JPA(07), JPA(09)-a0903 [light propagation]; Hehl AdP(08)-a0807; Bogolubov & Prykarpatsky a1204-in; Itin AP(12)-a1403 [jump conditions on an arbitrarily moving surface between two media]; Delphenich proc(15)-a1512 [as an approach to unification]; Pfeifer & Siemssen PRD(16)-a1602 [propagators, quantization].
@ History: Hehl & Obukhov GRG(05) [dimensions, units]; Hehl et al IJMPD(16)-a1607-conf [Kottler's program, and gravity]; Ni et al IJMPD(16)-a1611.
@ And spacetime metric: Gross & Rubilar PLA(01); Rubilar AdP(02)-a0706 [emergence of the light cone]; Itin & Hehl AP(04)gq [signature].
@ Variants: Donev & Tashkova JGSP-a1603 [non-linear extended electrodynamics].

Other Approaches > s.a. duality; parametrized formulation; Riemann-Silberstein Vector; self-dual fields.
@ Spacetime 2-forms: Gogberashvili JPA(06)ht/05, De Nicola & Tulczyjew IJGMP(09)-a0704 [variational, in terms of de Rham even and odd forms]; Itin & Friedman AdP(08)-a0808 [different possible 3+1 forms]; da Rocha & Rodrigues AdP(10)-a0811, comment Itin et al AdP(10)-a0911 [pair and impair, even and odd forms]; Grigorescu a0912.
@ Other manifestly covariant: Hillion NCB(99); Marmo & Tulczyjew RPMP(06)-a0708 [and introduction of particles]; Charap 11.
@ Quaternionic: Kravchenko in(03)mp/02; Jack mp/03.
@ Octonionic: Tolan et al NCB(06); Mironov & Mironov JMP(09); Nurowski a0906 [in terms of split octonions]; Chanyal et al IJTP(10)-a0910; Pushpa & Barata a1310 [fully symmetric Maxwell equations].
@ Other formulations: Harmuth et al 01 [magnetic dipole currents??]; 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 AIP(06)phy/04 [in terms of two 2-component relativistic fluids]; De Montigny & Rousseaux EJP(06)phy/05 [non-relativistic limits]; Pierseaux & Rousseaux phy/06; Re Fiorentin NCB(08)-a0905; Zalesny IJTP(09) [in Dirac-equation form, and moving dielectrics]; Kisel et al RicMat(11)-a0906-in [matrix formalism]; Bogolubov et al TMP(09) [and vacuum structure]; Gill & Zachary FP(11)-a1009; Heras EJP(10) [without assuming the c equivalence principle]; Wong a1012 [Lorenz's theory]; Yerchuck et al a1101 [complex-field formulation]; Aste JGSP(12)-a1211 [mass term and relativistic invariance]; Escalante & Tzompantzi IJPAM(12)-a1301 [alternative action, Hamiltonian analysis]; Nasmith a1306 [for an observer travelling at constant velocity through an isotropic medium]; Rajagopal & Ghose a1409 [Koopman-von Neumann formalism]; > s.a. Clebsch Potential.

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

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