Reduction and Coherent States

TL;DR

This paper introduces a quantum dimensional reduction technique applied to Gaussian coherent states, resulting in a family of semi-classical squeezed spin states with proven norm estimates and propagation properties.

Contribution

It presents a novel quantum reduction method to construct semi-classical squeezed states on complex projective spaces, expanding the understanding of coherent state transformations.

Findings

Established a symbol calculus for the new states

Proved semiclassical norm estimates for the states

Demonstrated propagation properties of the states

Abstract

We apply a quantum version of dimensional reduction to Gaussian coherent states in Bargmann space to obtain squeezed states on complex projective spaces. This leads to a definition of a family of squeezed spin states with excellent semi-classical properties, governed by a symbol calculus. We prove semiclassical norm estimates and a propagation result.