Carrying out the integration, one eliminates all the terms containing odd degree in

the direction cosines and obtains


 a 'Tabdzb
/ 4x


 a' 2 b [ ret a'] 'c"


+ j V[bGadva'] c" (Tr)d/ "- efa'b' dr + 0(e).
 T(2-53dv
 (2-153)


The divergent term in Eq. (2-153) has the same kinematical structure as the

mass term in Eq. (2-146). Therefore, it has the effect of an unobservable mass

renormalization, and by introducing the observed mass


 S02 -1
m = mo + lim -e
 e-o 2


(2-154)


one may now rewrite Eq. (2-146) as


/f bIZ'

+e2 b/ rt
 -0C


V[bGreta'] c"1 (1)"dr" + J v, [badv a'] c" 1
 (2-dv55)
 (2-155)


Then, substituting Eqs. (2-124) and (2-148) together with (2-151) into Eq. (2-155)

and using Eqs. (2-103) and (2-105), one finally obtains the equations of motion for

the electric charge 1 :



 1 The result shown here is the modified version by Hobbs [15] and is slightly dif-
ferent from the original, Eq. (5.26) in Dewitt and Brehme [3]. This is due to the
corrections made to Eqs. (5.12) and (5.14) in Dewitt and Brehme, whose modified
forms are now Eqs. (2-147) and (2-148), respectively.


mz