Classical Limits of Unbounded Quantities by Strict Quantization

TL;DR

This paper develops a framework using strict quantization to analyze the classical limits of unbounded operators in quantum theories, especially in bosonic quantum field theories, in a representation-independent way.

Contribution

It introduces a new approach for studying classical limits of unbounded quantities that works across different quantum representations.

Findings

Framework for classical limits of unbounded operators

Application to bosonic quantum field theories

Comparison of quantities in different Fock space representations

Abstract

This paper extends the tools of C*-algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories. We introduce the approach first in the simple case of finite systems. Then we apply this approach to analyze the classical limits of unbounded quantities in bosonic quantum field theories with particular attention to number operators and Hamiltonians. The methods take classical limits in a representation-independent manner and so allow one to compare quantities appearing in inequivalent Fock space representations.