Comment on 'Semiclassical dynamics of a spin-1/2 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 s u(2) coherent-state path integral for the quantum propagator P := (z(F)\ T exp(-i integral(0)(tau) H ds)\ z(1)) becomes exact, provided H is a linear combination of the su(2) generators with arbitrary time-dependent coefficie nts. I find the derivation of this in fact obvious result unduly complicate d and somewhat obscure. The authors start from a classical spin action inco nsistent with necessary boundary conditions and therefore are forced to inv oke a nontrivial regularization of the action to render the latter meaningf ul. Alternatively, when a su(2) symplectic potential consistent with the bo undary conditions is employed, no regularization is required to obtain the leading quasiclassical asymptotics.