  Several different methods have recently been proposed for calculating the
motion of a point particle coupled to a linearized gravitational field on a
curved background. These proposals are motivated by the hope that the point
particle system will accurately model certain astrophysical systems which are
promising candidates for observation by the new generation of gravitational
wave detectors. Because of its mathematical simplicity, the analogous system
consisting of a point particle coupled to a scalar field provides a useful
context in which to investigate these proposed methods. In this paper, we
generalize the axiomatic approach of Quinn and Wald in order to produce a
general expression for the self force on a point particle coupled to a scalar
field following an arbitrary trajectory on a curved background. Our equation
includes the leading order effects of the particle's own fields, commonly
referred to as ``self force'' or ``radiation reaction'' effects. We then
explore the equations of motion which follow from this expression in the
absence of non-scalar forces.
