A (t(x) 47 G"ret(x, z) Ja'(z)d4z, (2-117)

 adv(x) 4 Gad(, z ()d4z, (2-118)

by which the advanced and retarded fields of the particle are written

 re ret A Aret (2-119)
 b b;a a;b,

 Fadv Aadv Aadv (2-120)
 b -a b;a a;b

 The total field may be expressed in the forms


 Fab F + Fret out adv. (2-121)
 Fab Fab + ab ab + Fab (2

Alternatively, one may express the total field in the form


 Fab fab + Fab, (2-122)

where


 Fab 2 Ft+ F2adv) (2-123)

 fab Fa + Fout

 S l1" rad Rout 1 rad (-124)
 iab + 2Fab ab ab (2-124)
 2 2
 F rad Fret _adv (2-125)
 ab ab Fa- .(2-125)

Similarly to Eqs. (2-119) and (2-120), the fields Fab and Fard may be expressed in

terms of potentials Aa and Arad which are defined by the integral expressions of

the form (2-117) and (2-118), involving the functions Gaa' and Grada,, respectively.

The various fields defined thus satisfy the equations


gl/2Fretab;b gl/2Fadvab;b gl/2Fab;b 4= 4


(2-126)