Electromagnetic energy tensors and the Lorentz equation of motion for fields with electric and magnetic charge distributions

Abstract

In special or general relativity the electromagnetic energy tensor is usually taken to be ϑab = (1/4π)(FacFbc−(1/4) gabFcdFcd). This expression may also be used in the generalized theory which allows magnetic as well as electric charge. Rund [J. Math. Phys. 18, 84 and 1312 (1977)] has suggested a new approach to the generalized theory with an alternative form for the energy tensor. We show that in Rund’s theory there are other possible definitions for the energy tensor. However, there is a strong indication that a particular energy tensor gives rise in a definite way to a corresponding Lorentz equation of motion. This equation is derived for each of the energy tensors and it is found that only ϑab gives the Lorentz equation which is usually assumed in the generalized theory. Furthermore, the Lorentz equations arising from the other energy tensors will not give charge quantization.