Classical
Electromagnetism| 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.
Related Concepts > s.a. electricity [charge,
current]; electromagnetism with media and solutions; locality; magnetism; self-force.
* Energy: The self-energy in a charge distribution 
is
U = 
(r)
(r')
|r–r'|–1 dv dv'
.
@ 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]; > s.a. Chevreton
Tensor.
@ 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.
> Specific concepts:
see angular momentum; Debye
Length; Field Lines; Lorentz
Force; multipoles; Poynting
Vector; Wavelet.
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)jun];
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)apr];
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 AdP-gq/00;
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].
@ 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)jun
[boundary conditions];
Ridgely AJP(99)may
[Fab vs
Fab];
Malament
SHPMP(04)gq/03,
Leeds PhSc(06)oct
[T-reversal, B 
–B];
Goulart & Falciano IJMPA(09)-a0807
[and gravitation]; > s.a. integrable systems.
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send feedback and suggestions to bombelli at olemiss.edu – modified 17
oct
2009