  In a recent work, we presented the first application of the
Poisson-Wiseman-Anderson method of `matched expansions' to compute the
self-force acting on a point particle moving in a curved spacetime. The method
employs two expansions for the Green function which are respectively valid in
the `quasilocal' and `distant past' regimes, and which may be matched together
within the normal neighbourhood. In this article, we introduce the method of
matched expansions and discuss transport equation methods for the calculation
of the Green function in the quasilocal region. These methods allow the Green
function to be evaluated throughout the normal neighborhood and are also
relevant to a broad range of problems from radiation reaction to quantum field
theory in curved spacetime and quantum gravity.
