Quantum Weak Energy Inequalities for the Dirac field in Flat Spacetime

TL;DR

This paper derives an explicit quantum weak energy inequality bound for Dirac fields in flat spacetime, providing a concrete measure of quantum energy constraints for fermionic fields.

Contribution

It introduces a new explicit QWEI bound for Dirac fields in Minkowski space, extending previous theoretical results with a practical formula.

Findings

Derived an explicit QWEI bound for Dirac fields

Compared QWEI bounds across different quantum fields

Enhanced understanding of quantum energy constraints for fermions

Abstract

Quantum Weak Energy Inequalities (QWEIs) have been established for a variety of quantum field theories in both flat and curved spacetimes. Dirac fields are known (by a result of Fewster and Verch) to satisfy QWEIs under very general circumstances. However this result does not provide an explicit formula for the QWEI bound, so its magnitude has not previously been determined. In this paper we present a new and explicit QWEI bound for Dirac fields of arbitrary mass in four-dimensional Minkowski space. We follow the methods employed by Fewster and Eveson for the scalar field, modified to take account of anticommutation relations. A key ingredient is an identity for Fourier transforms established by Fewster and Verch. We also compare our QWEI with those previously obtained for scalar and spin-1 fields.