Multi-Periodic Coherent States and the WKB-Exactness

TL;DR

This paper develops a path integral formulation using multi-periodic coherent states for spin systems, demonstrating that the leading order approximation becomes exact in the large spin limit, and clarifies the relation between different trace formulas.

Contribution

It introduces a new multi-periodic coherent state path integral and proves its exactness in the large spin limit, extending previous formulations.

Findings

Exact calculation of the path integral formula.

Leading order matches the exact result for large spin.

Explicit correspondence between trace formulas.

Abstract

We construct the path integral formula in terms of ``multi-periodic'' coherent state as an extension of the Nielsen-Rohrlich formula for spin. We make an exact calculation of the formula and show that, when a parameter corresponding to the magnitude of spin becomes large, the leading order term of the expansion coincides with the exact result. We also give an explicit correspondence between the trace formula in the multi-periodic coherent state and the one in the ``generalized'' coherent state.