Classical Electromagnetism  

In General > s.a. Ampère's, Coulomb's and Faraday's Law; history of physics; lagrangian systems.
* Idea: The Abelian U(1) gauge theory of the electromagnetic interaction, governed by the Maxwell equations.
* Lagrangian approach: The Lagrangian density \({\cal L} = -{1\over4}|g|^{1/2} F_{ab}^{~} F^{ab}\) 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.

blue bullet Dynamics and solutions: see dynamics / field equations [including variables and transformation laws]; electromagnetism in media and solutions.
blue bullet Variations and generalizations: see alternative formulations; curved-spacetime version; modified theories of electromagnetism.

Related Concepts > s.a. electricity [charge, current]; locality; magnetism [field, magnetic potential, dipole moment]; self-force.
* Energy: The self-energy in a charge distribution ρ is

\[ U = \textstyle{1\over2} \int\rho({\bf r})\, \rho({\bf r}') |r-r'|^{-1}{\rm d}v\,{\rm d}v'\;.\]

@ Energy and momentum: Romer AJP(95)sep-Q [field]; Hnizdo AJP(97)jan [charged body]; Kislev & Vaidman AJP(02)dec [and causality]; Obukhov & Hehl PLA(03)phy [tensors]; López-Mariño & Jiménez FPL(04) [momentum density]; > s.a. energy-momentum tensor.
@ Conservation laws: Anco & Bluman JMP(97) [non-local]; Anco & Pohjanpelto AAM(01)mp [classification]; Bhatkar a2007 [asymptotic conservation law related to a subleading tail term]; > s.a. Chevreton and Zilch Tensor; conservation laws.
@ 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; Giuliani EJP(10)-a1005 [physical meaning]; Pati a1602 [measuring the vector potential]; > s.a. aharonov-bohm effect; connection; gauge choice.
@ Phenomenology: Goulart & Falciano IJMPA(09)-a0807 [and gravitation]; > s.a. spin-1 field theories.
> Specific concepts: see angular momentum; Debye Length; Field Lines; Liénard-Wiechert Potentials; Lorentz Force; multipoles; Poynting Vector; Wavelet.

Other References > s.a. computational physics; field theory.
@ Books, I: Bergmann 62.
@ Books, II: Solymar 84; Lim 86; Cottingham & Greenwood 91; Reitz et al 93; Westgard 96; Griffiths 98; Stewart 01; Pollack & Stump 01 [r AJP(05)jun]; Vanderlinde 04; Chaichian et al 11; Purcell 11; Bleaney & Bleaney 13; Purcell & Morin 13; Kuehn 16 [historical, based on foundational texts]; Lacava 16; Nolting 16.
@ Books, III: Stratton 41; Landau & Lifshitz v2, v8; Panofsky & Phillips 62; Eyges 72; Schwartz 72; Greiner 98; Jackson 98; Schwinger et al 98; Melia 01; Di Bartolo 04; Hehl & Obukhov 03 [from foundations]; Brau 04 [problems, r AJP(06)apr]; Franklin 05; Müller-Kirsten 11; Helrich 12; in Scheck 12; Garg 12; Zangwill 12; Englert 14 [esp. radiation]; Wilcox & Thron 16 + solutions manual [macroscopic]; Lechner 18.
@ Books: Maxwell 1877; Thomson 1895; O'Rahilly 38; de Groot & Suttorp 72; Pauli 73; Dugdale 93.
@ 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]; Garrity 15 [mathematical aspects].
@ Foundations: Maxwell PTRS(1865); Haugan & Lämmerzahl AdP-gq/00; Lämmerzahl ch(01); Hehl & Obukhov phy/00 [D, H, E, B]; Frisch PhSc(04)oct, reply Muller PhSc(07)apr, follow-up Vickers BJPS(08)-a0711 [inconsistency]; Frisch PhSc(08)jan [conceptual problems]; Leuchs et al APB(10)-a1005 [permittivity and permeability of free space from quantum vacuum]; Ni a1109-ch [Post-Maxwellian framework for corrections]; Ni et al MPLA(13)-a1204-conf [equivalence principle and cosmic interactions]; Frisch SHPMP(13) [conceptual problems]; Steane AJP(15)mar-a1402 [consistency]; Heras & Heras EJP(20)-a2006 [Feynman's approach, introducing potentials before fields].
@ Knotted solutions: Rañada JPA(90); Chiu & Moffatt PRS(95) [knotted B lines, energy]; Rañada & Trueba PLA(95), PLA(97); Arrayás & Trueba JPA(15)-a1106; Kedia et al PRL(13)-a1302; Hoyos et al JPA(15)-a1502 [new solutions]; Alves et al PLB(17)-a1705 [including generalizations of Maxwell theory]; Nastase & Sonnenschein FdP(18)-a1802 [Lagrangian formulation, generalizations and quantization]; Vancea a1911-in [rev, and generalization to non-linear electrodynamics]; Goulart & Ottoni a2004 [unified description].
@ Other topological features: Singleton IJTP(95)ht/97 [topological electric charge]; Rañada AdP(12); > s.a. charge.
@ Time reversal: Malament SHPMP(04)gq/03, Leeds PhSc(06)oct [and B \(\mapsto\) −B]; Weinstein MPLA(11)-a1004, Boozer AJP(13)aug [and time asymmetry].
@ Boundary conditions: Hall AJP(95)jun; McNees & Gangopadhyaya AJP(14)jun [electric field, chargeless interface between two regions of space].
@ Related topics: Vaidya & Farina PLA(91) [and Galilean mechanics]; Ridgely AJP(99)may [\(F_{ab}\) vs \(F^{ab}\)]; Escobar & Urrutia JMP(14)-a1309 [gauge-invariant Lorentz scalars]; > s.a. integrable systems.

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