On the Removal of Divergences in Electrodynamics: A Global Point of View

F. Hoyle, J. V. Narlikar
1993 Proceedings of the Royal Society A  
This paper explores the implications of Dirac's seminal work on the concept of selfenergy of a charged particle in classical electrodynamics. To avoid the notion of divergent acceleration through self-action, Dirac offered an alternative that involved the existence of preacceleration and an apparent departure from the inherent causality of special relativity. It is argued that Dirac's solution appears naturally in the electrodynamics described by action at a distance. In this framework the
more » ... n of self-action is replaced by that of the response of the universe on the large scale. Provided the universe has the correct large-scale structure, there are no divergent integrals either in the classical or the quantum version of electrodynamics. The price one has to pay involves replacing the purely local Lorentz invariant picture by a global cosmological one. On the other hand the price of standard renormalizable quantum electrodynamics is that of the theoretical mass of the electron is infinitely negative, a requirement that Dirac regarded as absurd, far worse than the loss of local invariance in favour of global invariance, the position adopted here. j^(a)ikdai(d5 F(ka)ik = 4~e J4(X, A)sa d8a -4j(a)i(1 where Xx(i) is a general point with coordinates xi and A -(ai) is a typical point
doi:10.1098/rspa.1993.0115 fatcat:722hrh3ikvdwvnzs6cmfu7rcby