Quantum cutting and a Szeg\"o limit theorem

TL;DR

This paper develops a quantum analogue of symplectic cutting using semiclassical pseudodifferential operators and proves a Szeg"o limit theorem within this framework, advancing the mathematical understanding of quantum symplectic geometry.

Contribution

It introduces a novel algebra of semiclassical pseudodifferential operators as a quantum analogue of symplectic cutting and establishes a Szeg"o limit theorem for this setting.

Findings

Construction of a new algebra of semiclassical pseudodifferential operators

Proof of a Szeg"o limit theorem in the quantum symplectic cutting context

Extension of classical symplectic cutting concepts to quantum setting

Abstract

Given a representation of the circle group by semiclassical Fourier integral operators, we construct an algebra of semiclassical pseudodifferential operators that are a quantum analogue of the notion of symplectic cutting of Lerman, and we prove an associated Szeg\"o limit theorem.