2 1
m" = ebF a +bin 2 e2(a 2a) + 2 (R b + aRbc bc)
3 3
ret
+2b V[bGret a]C (z (T), z (T')) c' (T')dT'. (2-56)
The integral term involving this Green's function in Eq. (2-156), often referred
to as the "tail" term, gives an implication that the motion of the particle is affected
by the entire history of the particle itself. This, together with the third term on
the right hand side will make the particle deviate from its original world-line to
the order of e2, even in the absence of an external incident field Fabin, which means
that radiation damping is expected to occur even for a particle in free fall in curved
spacetime.