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