Formulations of Maxwell's Theory| 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 PRA(16)-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];
De Luca et al EJP(19)-a1902 [Feynman's other approach],
a2001 [and other treatments].
@ 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 CQG(17)-a1507 [5D Kaluza-Klein theory];
Kulyabov et al a2002 [Finsler approach];
> 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];
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];
Fewster et al PRD(18)-a1709 [Quantum Energy Inequalities].
@ 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.
@ Phenomenology: Itin PRD(05)ht [vacuum no-birefringence conditions],
JPA(07),
JPA(09)-a0903 [light propagation].
@ 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 IJGMP-a1310 [fully symmetric Maxwell equations].
@ Lorenz's theory: Wong a1012;
Kragh a1803 [1867 paper and annotations];
> s.a. history of physics.
@ 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];
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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