Also we have the field Fbv derived from another solution of Eqs. (2-2) and

(2-3), which is provided by the advanced potentials. F.db is expected to p1 li a

symmetrical role to Fr in all questions of general theory. Thus, corresponding to

Eq. (2-7) one may put
 Fab ab + Fab (2-8)
 act (2adv out-)

where a new field Fbt is expected to p1' v a symmetrical role in general theory

to Fib, and should be interpretable as the field of outgoing radiation leaving the

neighborhood of the electron. The difference
 Fab ab pab -9)
 rad out in (2-9)

would then be the field of radiation produced by the electron. Alternatively, from

Eqs. (2-7) and (2-8), this difference may be expressed as


 Fbd = F F ,, (2-10)


which shows that F^ is completely determined by the world-line of the electron.

Through some calculations, it is found to be

 4e d3a dzb d3XbdX, ^on\
 Fabrad =- d3 db 3 tb ) (2-11)
 3 ( ds" ds ds" ds

near the world-line, and is free from singularity.

 With the attained symmetry between the use of retarded and advanced fields,

one defines a field

 fab (Fab ab a Fbv) (2-12)

which will be used to describe the motion of the electron. This field is derivable

from potentials satisfying Eq. (2-6) and is free from singularity on the world-line of

the electron. From Eqs. (2-7) and (2-8), it is in fact just the mean of the incoming