No-go theorem for the classical Maxwell-Lorentz electrodynamics in odd-dimensional worlds
Escuela de Física, Universidad Autónoma de Zacatecas - Apartado Postal C-580 Zacatecas 98068, Zacatecas, Mexico
2 Russian Federal Nuclear Center - Sarov, 607190 Nizhnii Novgorod Region, Russia
Accepted: 27 October 2011
If the conventional Maxwell-Lorentz formulation of classical electrodynamics is adopted in a flat spacetime of arbitrary odd dimension, then the retarded vector potential Aμ generated by a point charge turns out to be pure gauge, Aμ=∂μχ. By Gauss' law, the charge shows up as zero. The classical electromagnetic coupling is thus missing from odd-dimensional worlds. If the action is augmented by the addition of the Chern-Simons term, then the classical interaction picture in the three-dimensional world becomes nontrivial.
PACS: 03.50.De – Classical electromagnetism, Maxwell equations / 11.10.Kk – Field theories in dimensions other than four
© EPLA, 2011