On the extra phase correction to the semiclassical spin coherent-state propagator

TL;DR

This paper investigates the origin of the Solary-Kochetov extra-phase in semiclassical spin coherent-state propagators, clarifying its derivation using the Holstein-Primakoff representation for su(2) spins.

Contribution

It demonstrates that the extra-phase correction arises from the difference between principal and Weyl symbols in the spin case when using the Holstein-Primakoff representation.

Findings

Extra-phase correction linked to principal and Weyl symbol difference.

Holstein-Primakoff representation clarifies the correction's origin.

Applicable to semiclassical spin propagators in phase space.

Abstract

The problem of an origin of the Solary-Kochetov extra-phase contribution to the naive semiclassical form of a generalized phase-space propagator is addressed with the special reference to the su(2) spin case which is the most important in applications. While the extra-phase correction to a flat phase-space propagator can straightforwardly be shown to appear as a difference between the principal and the Weyl symbols of a Hamiltonian in the next-to-leading order expansion in the semiclassical parameter, the same statement for the semiclassical spin coherent-state propagator holds provided the Holstein-Primakoff representation of the su(2) algebra generators is employed.