Poincaré invariance—classical electrodynamics

Abstract

In a previous paper by the authors [J. Math. Phys. 29, 1361 (1988)] it was shown that, following the standard definition, the angular momentum tensor corresponding to the Coulomb field does not exist (due to the long range of the field). In the present paper, for a general classical field theory, nonconventional definitions for the four-momentum and angular momentum tensor are given. These definitions are applied to the particular case of a charged classical point particle in an external electromagnetic field, showing that the total four-momentum Pμ and the total angular momentum tensor Mλμ of the system exist and are conserved quantities. In this framework, no asymptotic conditions on the four-acceleration of the particle are needed. The problem of extracting an equation of motion for the particle from these conservation laws is discussed. Also, the different parts (such as the radiated one and the bound one) of Pμ and Mλμ, and their corresponding energy momentum tensors and angular momentum density tensors, are considered.