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.
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')
|r–r'|–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].
Main page – Abbreviations – Journals – Comments – Other
sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified
12 jul 2008