  We develop a new method of computing radiation reaction for a point particle
interacting with massless scalar and vector fields in curved space-time. It is
based on the analysis of field Green's functions with both points lying on the
particle world-line and does not require integration of the field stresses
outside the world line as was used in the DeWitt-Brehme approach, thus leading
to a substantial simplification of the problem. We start with space-time of an
arbitrary dimension and show that the Hadamard expansion of the massless scalar
and vector Green's functions contain only integer inverse powers of the Synge
world function in even dimensions and only half-integer in the odd dimensions.
The even-dimensional case then is treated in detail. We analyze divergencies,
calculate higher-derivative counterterms, and find a recurrent formula for the
local parts of the reaction force in neighboring dimensions. Higher-dimensional
curved space counterterms are not simply the covariant generalizations of the
flat ones, but contain additional curvature-dependent terms. We illustrate our
formalism in four and six dimensions. In the first case we rederive the results
of DeWitt-Brehme-Hobbs in a simpler way, in the second case we give a covariant
generalization of the Kosyakov equation. The local part of the reaction force
is found to contain a term proportional to the Riemann tensor which is absent
in four dimensions.

General Relativity and Quantum Cosmology;High Energy Physics - Theory