Classical Electromagnetism  

In General > s.a. Ampère's, Coulomb's, Faraday's Law; dynamics; history; lagrangian systems.
* Idea: The Abelian U(1) gauge theory of the electromagnetic interaction, governed by the Maxwell equations.
* Lagrangian approach: = – |g|1/2 Fab Fab, which is proportional to the second Chern class of the curvature of A; Varying the action one gets the equations with sources, "metric" equations, while the others are the Bianchi identities and have to do with topology and the fact that F = dA.
* Symmetries: The equations are conformally invariant in D = 4 dimensions, but not for an arbitrary D; > s.a. conformal invariance.

With Matter / In Extended Media > s.a. astrophysics; energy-momentum; light; monopoles; radiation; Thomas Precession.
* Electroacoustic effect: When an acoustic wave propagates through an electrically conducting surface, it can drag electric charge along with it, just as wind drags autumn leaves along a street.
@ Extended media and objects: Hertzberg et al AJP(01)gq [rotating dielectric and special relativity]; Tip JMP(06) [dispersive and absorptive]; Red'kov & Spix ht/06-in [moving, uniform]; Stoeckel mp/07 [extended charged particle in electromagnetic field, covariant equations of motion]; Ravndal a0804 [effective theory]; Leung & Ni EJP(08) [on derivation].
@ Non-linear media: Babin & Figotin CMP(03); Konopelchenko & Moro JPA(04) [geometric optics].
@ Inhomogeneous media: Kravchenko mp/01 [quaternion formulation]; Dereli et al PLA(07) [covariant framework]; > s.a. radiation.
@ Waves in other media: Kravchenko & Oviedo mp/01 [chiral]; De Lorenci & Souza PLB(01)gq [effective geometry].
@ Fields: Masmoudi & Nakanishi CMP(03) [Maxwell-Dirac and Maxwell-Klein-Gordon, uniqueness].
@ Point sources: Marino AP(02)phy/01; Boyer FP(02) [and Aharonov-Bohm phase]; Chen et al CPL(03)ht/01 [magnetic sources]; Moulin NCB(01)mp/02 [monopoles]; Silbergleit et al JMP(03)mp [surface point charge singularities]; Gabrielov et al mp/04 [equilibrium points]; > s.a. distributions, self-force.
@ Related topics: Ilisavskii et al PRL(01) + pn(01)sep [anomalous electroacoustic effect].

Related Areas and Concepts > s.a. angular momentum; electricity; locality; Lorentz Force; magnetism; self-force.
* Energy: The self-energy in a charge distribution is

U =  (r) (r') |rr'|–1 dv dv' .

@ Energy and momentum: Romer AJP(95)Q [field]; Hnizdo AJP(97) [charged body]; Kislev & Vaidman AJP(02) [and causality]; Obukhov & Hehl PLA(03)phy [tensors]; López-Mariño & Jiménez FPL(04) [momentum density]; > s.a. energy-momentum.
@ Conservation laws: Anco & Bluman JMP(97) [non-local]; Anco & Pohjanpelto AAM(01)mp [classification]; > s.a. Chevreton.
@ Potential effects: Líu qp/95, qp/95; Anco & The AAM(05)mp [and conservation laws]; Rousseaux phy/05 [magnetic torque], AFLB(05)phy, phy/05; > s.a. connection; gauge choice; Liénard-Wiechert Potentials; modified electromagnetism.
@ Retarded fields: & Chubykalo & Vlaev, comment Skovrlj & Ivezic IJMPA(02), Jackson IJMPA(02).
@ Dipoles: Anandan Nat(97)ht/98, PRL(00)ht/99 [interactions]; Power & Thirunamachandran PRS(01), PRS(01) [field]; Pospelov & Ritz AP(05) [values, and CP violation]; Troncoso & Curilef EJP(06) [in a magnetic field]; > s.a. distributions.
> Specific concepts: see Debye Length; Field Lines; multipoles; Poynting Vector; Wavelet.

Methods and Solutions > s.a. curved spacetime; gauge theory solutions [spherical]; laplace equation; lattice gauge theories.
* Remark: There are only 11 separable problems (coordinate systems), only 4 of which are not axisymmetric.
@ Zero-energy solution: Chubykalo MPLA(98); Dvoeglazov phy/99-in.
@ Superluminal solutions: Capelas de Oliveira & Rodrigues PLA(01)mp; Zamboni-Rached et al PRE(01)phy/00, EPJD(02)phy/01, phy/02 [wave guide].
@ Other solutions: Katsenelenbaum SPU(94) [approximate]; Bialynicki-Birula & Bialynicka-Birula PRA(03) [with vortex lines]; Lynden-Bell PRD(04) [relativistic rotating disk]; Huttunen et al JCP(07) [ultra weak variational formulation].
@ Waves: Walker & Dual gq/97 [longitudinal, near field]; Bicák & Schmidt PRD(07)-a0803 [with helical symmetry]; > s.a. particles [field configurations as particle models]; wave phenomenology.
@ Boundary value problems: Balean & Bartnik PRS(98) [null/timelike boundary]; Reula & Sarbach gq/04 [as model for general relativity].
@ Related topics: Ferraro AJP(97) [Lorentz transformations]; Mosley JMP(98) [two complex U's]; Costa De Beauregard FP(04) [status/measurement of A]; Moses JMP(04) [using irreps of Poincaré group]; > s.a. aharonov-bohm effect.
> Related topics: see duality; fluctuations; forms; Image Charge; paradigms in physics [hierarchical]; solitons; Thomson Scattering.

Other References > s.a. alternative formulations; computational physics; field theory.
@ Books, I/II: Bergmann 62 [I]; Solymar 84; Lim 86; Reitz et al 93; Westgard 96; Griffiths 98; Stewart 01; Pollack & Stump 02 [r AJP(05)]; Vanderlinde 04 [II].
@ Books, III: Stratton 41; Landau & Lifshitz 60; Panofsky & Phillips 62; Eyges 72; Schwartz (97); Greiner 98; Jackson 98; Schwinger et al 98; Melia 01; Di Bartolo 03; Hehl & Obukhov 03 [from foundations]; Muller-Kirsten 04; Brau 04 [problems, r AJP(06)]; Franklin 05.
@ Books: Maxwell 1877; Thomson 04; O'Rahilly 38; de Groot & Suttorp 72; Dugdale 93; Pauli & Enz (00).
@ Books, special emphasis: in Hodge 52 [De Rham approach]; Barut 64 [relativistic]; Lim 93 [problems and solutions]; Parrott 87 [and differential geometry]; Baylis 98 [Clifford algebra]; in Baez & Muniain 94 [and differential geometry]; Kalluri 98 [and engineering].
@ Foundations: Haugan & Lämmerzahl gq/00/AdP; Hehl & Obukhov phy/00 [D, H, E, B]; Frisch PhSc(04), reply Muller PhSc(07), follow-up Vickers a0711-BJPS [inconsistency].
@ Topological features: Rañada JPA(90) [knotted solutions]; Chiu & Moffatt PRS(95) [knotted B lines, energy]; Rañada & Trueba PLA(95), PLA(97); Singleton IJTP(95)ht/97 [topological electric charge]; > s.a. charge.
@ Related topics: Vaidya & Farina PLA(91) [and Galilean mechanics]; Hall AJP(95) [boundary conditions]; Ridgely AJP(99) [Fab vs Fab]; Malament SHPMP(04)gq/03, Leeds PhSc(06) [T-reversal, B B].


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