no /j /2gaa',gbb' a'/b' (4) dT,


(47)-1 g1/2 (FacFbc


The divergences of these tensors are found to be


-m0 a' g a'b (g1/2(4);b, d

e 12 /2 aF a'b' b'(4)dT


mo J /S2ga'"a'd (4)dT


Fa bb,



(47r) 1 ;b b (Fd;b Fdb;c + Fbc;d) Fcd

-Fabb.


Combining these results, one obtains the conservation law



 Ta;b = 0.

 Vector potentials and electromagnetic fields.


(2-112)


(2-113)


(2-114)


In the Lorenz gauge


gabAa;b = 0,


(2-115)


the electromagnetic field equation (2-107) may be rewritten as an inhomogeneous

vector wave equation


(2-116)


Particular solutions of this equation are given by


where


Tab
particle

 Trab
 field


1 ab aFcdF
4 )


(2-110)

(2-111)


rab
particle;b


47a g12 (gbcAabc RabA b)