  We formulate a new analytical method for regularizing the self-force acting
on a particle of small mass $\mu$ orbiting a black hole of mass $M$, where
$\mu\ll M$. At first order in $\mu$, the geometry is perturbed and the motion
of the particle is affected by its self-force. The self-force, however,
diverges at the location of the particle, and hence should be regularized. It
is known that the properly regularized self-force is given by the tail part (or
the $R$-part) of the self-field, obtained by subtracting the direct part (or
the $S$-part) from the full self-field. The most successful method of
regularization proposed so far relies on the spherical harmonic decomposition
of the self-force, the so-called mode-sum regularization or mode decomposition
regularization. However, except for some special orbits, no systematic
analytical method for computing the regularized self-force has been given. In
this paper, utilizing a new decomposition of the retarded Green function in the
frequency domain, we formulate a systematic method for the computation of the
self-force. Our method relies on the post-Newtonian (PN) expansion but the
order of the expansion can be arbitrarily high. To demonstrate the essence of
our method, in this paper, we focus on a scalar charged particle on the
Schwarzschild background. The generalization to the gravitational case is
straightforward, except for some subtle issues related with the choice of gauge
(which exists irrespective of regularization methods).
