Quantum energy inequalities and local covariance II: Categorical formulation

TL;DR

This paper develops a categorical framework for Quantum Energy Inequalities within locally covariant quantum field theory, introducing new structural properties and covariant formulations of field spectra and functional calculus.

Contribution

It provides a categorical formulation of QEIs, introduces the concept of Local Physical Equivalence, and develops covariant spectral and functional calculus for quantum fields.

Findings

Formulated QEIs in a categorical framework

Identified Local Physical Equivalence as a structural property

Developed covariant spectral and functional calculus for fields

Abstract

We formulate Quantum Energy Inequalities (QEIs) in the framework of locally covariant quantum field theory developed by Brunetti, Fredenhagen and Verch, which is based on notions taken from category theory. This leads to a new viewpoint on the QEIs, and also to the identification of a new structural property of locally covariant quantum field theory, which we call Local Physical Equivalence. Covariant formulations of the numerical range and spectrum of locally covariant fields are given and investigated, and a new algebra of fields is identified, in which fields are treated independently of their realisation on particular spacetimes and manifestly covariant versions of the functional calculus may be formulated.