No-go theorem for the classical Maxwell-Lorentz electrodynamics in odd-dimensional worlds

Details No-go theorem for the classical Maxwell-Lorentz electrodynamics in odd-dimensional worlds No-go theorem for the classical Maxwell-Lorentz electrodynamics in odd-dimensional worlds

2002-08-23

arxiv.org/abs/hep-th/0208170v2

Physics

High Energy Physics

High Energy Physics - Theory

V1 LaTeX, 4 pages, V2. The title is changed, two new authors appear for the reason explained at the end of the text, the main

Scientific paper

If the conventional Maxwell--Lorentz formulation of classical electrodynamics is adopted in a flat spacetime of arbitrary odd dimension, then the retarded vector potential $A^\mu$ generated by a point charge turns out to be pure gauge, $A^\mu=\partial^\mu\chi$. 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.

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