Classical Electromagnetism| 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.
Dynamics
and solutions: see dynamics / field equations [including variables and transformation laws];
electromagnetism in media and solutions.
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
@ 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.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 18 jul 2020