Comment on 'Semiclassical dynamics of a spin-1/2 in an arbitrary magnetic field'

In a recent paper Alscher and Grabert claim to prove that a dominant (tree-level) stationary phase approximation to the Wiener regularized continuum su(2) coherent-state path integral for the quantum propagator P: becomes exact, provided H is a linear combination of the su(2) generators with arbitrary time-dependent coefficients. I find the derivation of this in fact obvious result unduly complicated and somewhat obscure. The authors start from a classical spin action inconsistent with necessary boundary conditions and therefore are forced to invoke a nontrivial regularization of the action to render the latter meaningful. Alternatively, when a su(2) symplectic potential consistent with the boundary conditions is employed, no regularization is required to obtain the leading quasiclassical asymptotics. (author)