ua nt - p h / 99 04 10 2 v 1 2 9 A pr 1 99 9 Semiclassical dynamics of a spin - 12 in an arbitrary magnetic field

The spin coherent state path integral describing the dynamics of a spin-12system in a magnetic field of arbitrary time-dependence is considered. Defining the path integral as the limit of a Wiener regularized expression, the semiclassical approximation leads to a continuous minimal action path with jumps at the endpoints. The resulting semiclassical propagator is shown to coincide with the exact quantum mechanical propagator. A non-linear transformation of the angle variables allows for a determination of the semiclassical path and the jumps without solving a boundary-value problem. The semiclassical spin dynamics is thus readily amenable to numerical methods. 03.65.Sq, 67.57.Lm, 31.15.Kb