Energy Inequalities in Quantum Field Theory

TL;DR

This paper reviews quantum energy inequalities, which are lower bounds on averaged energy densities in quantum field theory, highlighting their relation to classical energy conditions, thermodynamics, and quantum mechanics.

Contribution

It provides a comprehensive review of quantum energy inequalities and their connections to thermodynamics and quantum mechanics.

Findings

Quantum energy inequalities impose lower bounds on averaged stress-energy tensors.

These inequalities serve as quantum analogues of classical energy conditions.

Connections are established between quantum energy inequalities and thermodynamic principles.

Abstract

Quantum fields are known to violate all the pointwise energy conditions of classical general relativity. We review the subject of quantum energy inequalities: lower bounds satisfied by weighted averages of the stress-energy tensor, which may be regarded as the vestiges of the classical energy conditions after quantisation. Contact is also made with thermodynamics and related issues in quantum mechanics, where such inequalities find analogues in sharp Gaarding inequalities.