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

Andrew E. Chubykalo; Augusto Espinoza; B. P. Kosyakov

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arXiv · hep-th/0208170

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

Andrew E. Chubykalo·Augusto Espinoza·B. P. Kosyakov

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Abstract

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

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Andrew E. Chubykalo, Augusto Espinoza, B. P. Kosyakov. 2011-10-25. No-go theorem for the classical Maxwell-Lorentz electrodynamics in odd-dimensional worlds. https://arxiv.org/abs/hep-th/0208170

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