  We present a new, simple method for calculating the scalar, electromagnetic,
and gravitational self forces acting on particles in orbit around a Kerr black
hole. The standard ``mode-sum regularization'' approach for self-force
calculations relies on a decomposition of the full (retarded) perturbation
field into multipole modes, followed by the application of a certain
mode-by-mode regularization procedure. In recent years several groups have
developed numerical codes for calculating black hole perturbations directly in
2+1 dimensions (i.e., decomposing the azimuthal dependence into $m$-modes, but
refraining from a full multipole decomposition). Here we formulate a practical
scheme for constructing the self force directly from the 2+1-dimensional
$m$-modes. While the standard mode-sum method is serving well in calculations
of the self force in Schwarzschild geometry, the new scheme should allow a more
efficient treatment of the Kerr problem.
