More about Path Integral for Spin

TL;DR

This paper revisits the path integral formulation for SU(2) spin systems, demonstrating the equivalence of the Nielsen-Rohrlich formula to the coherent state approach and showing that the WKB approximation yields exact results.

Contribution

It establishes the equivalence between the Nielsen-Rohrlich formula and the spin coherent state formalism, clarifies the topology of the phase space, and proves the exactness of the WKB approximation for this system.

Findings

NR formula is equivalent to the coherent state expression

Phase space in NR formalism is topologically trivial

WKB approximation gives exact results

Abstract

Path integral for the $SU(2)$ spin system is reconsidered. We show that the Nielsen-Rohrlich(NR) formula is equivalent to the spin coherent state expression so that the phase space in the NR formalism is not topologically nontrivial. We also perform the WKB approximation in the NR formula and find that it gives the exact result.