Corrections to the coherent state path integral: Comments upon a speculation of L. S. Schulman

Abstract

Intuitively, the Feynman path integral corresponds to a weighted sum over classical paths, an interpretation that fails for the phase space path integral. To address the question of whether there exists a path integral expression conforming to a sum over paths in phase space, an examination of the discrete coherent state path integral (CSPI) is undertaken. Via an alternative formulation of the CSPI, it is shown that the coherent state action for a broad class Hamiltonians can be transformed from the variables (q,p) to (q,q̇). For these Hamiltonians, such a transformation along with the inclusion of all terms O(ε(zi−zi−1)) yields an expression which, for finite ε, can be interpreted as a sum over classical paths with Gaussian weight. The numerical evaluation of this expression through importance sampling (Monte Carlo) is demonstrated.