paper

Self-interaction in classical gauge theories and gravitation

arXiv:1812.03290 · doi:10.1016/j.physrep.2019.03.002

Abstract

To develop a systematic treatment of the self-interaction problem in classical gauge theories and general relativity, we study tenable manifestations of self-interaction: topological phases, and rearrangements of degrees of freedom appearing in the action. We outline the occurrence of topological phases in pure field systems. We show that the rearranged Maxwell-Lorentz electrodynamics is a mathematically consistent and physically satisfactory theory which describes new entities, dressed charged particles and radiation. We extend this analysis to cover different modifications of the Maxwell-Lorentz electrodynamics and the SU(N) Yang-Mills-Wong theory. We take a brief look at a subtle mechanism of self-interaction in classical strings. Turning to general relativity, we note that the total energy and momentum of a system with nontrivial topological content, such as a black hole, are ambiguous, coordinatization-dependent quantities, which resembles the situation with paradoxical decompositions in the Banach-Tarski theorem.

92 pages, 1 figure. This paper is written on the occasion of the 80th anniversary of publication of the 1938 Dirac's article "The classical theory of radiating electron", Proc. R. Soc. A167, 148, the outcome of which, known as the Abraham-Lorentz-Dirac equation, is one of the most controversial equations in the history of physics; v.3 accepted for publication in Physics Reports

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