itself. And the the second term (ii), defined as the radiation field, comes from the
homogeneous solution of the equation
]A, 0, (3-5)
and is completely responsible for the ALD force.
It turns out that in the absence of the incident field Fib, the only physical
solution of Eq. (3-1) is v' = 0, i.e. geodesic motion, hence there is no self-force on
the particle.
3.1.2 Dewitt and Brehme: Electromagnetic Radiation Damping in
Curved Spacetime
Dewitt and Brehme [3] generalized Dirac's approach [2] to the general curved
spacetime. Using the Hadamard expansion techniques for the vector field in curved
spacetime, the equation of motion for the charged particle turns out to be
2 1
mI" = ezbF bin + -e2 (a 32 a) + 1 2 (Rabb + %aRbcb c)
3 3
+ lim e2 b V[bVGret a]c/ (z(-T), z(-T)) c' (T)d-', (3-6)
where Ge (z(7), z(7')) is a bi-vector retarded Green's function for the vector wave
equation in curved spacetime
V2A et R R b et -47,J (3-7)
with the current density
Ja e I gaa (x, z(7)) va')(4) (x z(r)) d, (3-8)
(g9aa (x, z): bi-vector of geodesic parallel displacement).
The integral term involving this Green's function in Eq. (3-6) is often called
the I i!" part, giving an implication that the particle's motion is affected by the
entire history of the source. This tail term, together with the third term on the