Quantum Inequalities from Operator Product Expansions

TL;DR

This paper establishes quantum inequalities in general quantum field theories on Minkowski space using a rigorous operator product expansion, providing fundamental bounds on local quantum observables.

Contribution

It introduces a nonperturbative method to derive quantum inequalities in interacting quantum field theories via a rigorous operator product expansion.

Findings

Derived quantum inequalities for a broad class of quantum field theories.

Provided a nonperturbative framework for establishing bounds on local observables.

Extended the applicability of quantum inequalities beyond free theories.

Abstract

Quantum inequalities are lower bounds for local averages of quantum observables that have positive classical counterparts, such as the energy density or the Wick square. We establish such inequalities in general (possibly interacting) quantum field theories on Minkowski space, using nonperturbative techniques. Our main tool is a rigorous version of the operator product expansion.