A quantum weak energy inequality for the Dirac field in two-dimensional flat spacetime

TL;DR

This paper extends a quantum weak energy inequality for Dirac fields to two-dimensional flat spacetime, providing a non-optimal but broadly applicable bound that includes all non-negative masses.

Contribution

It adapts an existing inequality to two-dimensional spacetime, broadening its applicability and including all non-negative mass values.

Findings

The bound matches the order of magnitude of the optimal zero-mass case.

The inequality applies to all non-negative masses.

It is non-optimal but explicitly constructed.

Abstract

Fewster and Mistry have given an explicit, non-optimal quantum weak energy inequality that constrains the smeared energy density of Dirac fields in Minkowski spacetime. Here, their argument is adapted to the case of flat, two-dimensional spacetime. The non-optimal bound thereby obtained has the same order of magnitude, in the limit of zero mass, as the optimal bound of Vollick. In contrast with Vollick's bound, the bound presented here holds for all (non-negative) values of the field mass.