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