  A relativistic description of the Kapitza-Dirac effect in the so-called Bragg
regime with two and three interacting photons is presented by investigating
both numerical and perturbative solutions of the Dirac equation in momentum
space. We demonstrate that spin-flips can be observed in the two-photon and the
three-photon Kapitza-Dirac effect for certain parameters. During the
interaction with the laser field the electron's spin is rotated, and we give
explicit expressions for the rotation axis and the rotation angle. The
off-resonant Kapitza-Dirac effect, that is, when the Bragg condition is not
exactly fulfilled, is described by a generalized Rabi theory. We also analyze
the in-field quantum dynamics as obtained from the numerical solution of the
Dirac equation.
