  The motion of a small compact object in a curved background spacetime
deviates from a geodesic due to the action of its own field, giving rise to a
self-force. This self-force may be calculated by integrating the Green function
for the wave equation over the past worldline of the small object. We compute
the self-force in this way for the case of a scalar charge in Schwarzschild
spacetime, making use of the semi-analytic method of matched Green function
expansions. Inside a local neighbourhood of the compact object, this method
uses the Hadamard form for the Green function in order to render regularization
trivial. Outside this local neighbourhood, we calculate the Green function
using a spectral decomposition into poles (quasinormal modes) and a branch cut
integral in the complex-frequency plane. We show that both expansions overlap
in a sufficiently large matching region for an accurate calculation of the
self-force to be possible. The scalar case studied here is a useful and
illustrative toy-model for the gravitational case, which serves to model
astrophysical binary systems in the extreme mass-ratio limit.
