Stationary Phase in Coherent State Path Integrals

TL;DR

This paper clarifies that the stationary phase approximation in coherent state path integrals can be applied using paths satisfying equations of motion, even if they do not meet boundary conditions, simplifying the analysis.

Contribution

It demonstrates that reevaluating the action is unnecessary for applying stationary phase approximation, provided the path satisfies Lagrange's equations.

Findings

Stationary phase approximation applies without boundary condition satisfaction.

Paths satisfying equations of motion suffice for the approximation.

Reevaluation of the action is not required in this context.

Abstract

In applying the stationary phase approximation to coherent state path integrals a difficulty occurs; there are no classical paths that satisfy the boundary conditions of the path integral. Others have gotten around this problem by reevaluating the action. In this work it is shown that it is not necessary to reevaluate the action because the stationary phase approximation is applicable so long as the path, about which the expansion is performed, satisfies the associated Lagrange's equations of motion. It is not necessary for this path to satisfy the boundary conditions in order to apply the stationary phase approximation.