Title: On classical electrodynamics in odd-dimensional worlds
Abstract: Given the conventional Maxwell-Lorentz formulation of classical electrodynamics in a flat spacetime of arbitrary odd dimension, the retarded vector potential $A^\mu$ generated by a point-like charge is found to be pure gauge, $A^\mu=\partial^\mu\chi$. By the Gauss law, the charge vanishes. Therefore, classical electromagnetism is missing from odd-dimensional worlds. By contrast, a particle interacting with a scalar field generates nonzero field strength. If the electromagnetic action is augmented by the addition of the Chern-Simons term, the interaction picture in the three-dimensional world becomes nontrivial.
Publication Year: 2002
Publication Date: 2002-08-23
Language: en
Type: article
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