An absolute quantum energy inequality for the Dirac field in curved spacetime

TL;DR

This paper establishes the first absolute quantum energy inequality for the massive Dirac field in four-dimensional curved spacetimes, providing bounds based solely on local geometry rather than specific quantum states.

Contribution

It introduces an absolute QWEI for the Dirac field in curved spacetime, removing the dependence on arbitrary reference states.

Findings

Proves an absolute QWEI for the Dirac field in four dimensions.

Bounds depend only on local geometric properties.

Extends the understanding of quantum energy inequalities in curved spacetime.

Abstract

Quantum Weak Energy Inequalities (QWEIs) are results which limit the extent to which the smeared renormalised energy density of a quantum field can be negative. On globally hyperbolic spacetimes the massive quantum Dirac field is known to obey a QWEI in terms of a reference state chosen arbitrarily from the class of Hadamard states; however, there exist spacetimes of interest on which state-dependent bounds cannot be evaluated. In this paper we prove the first QWEI for the massive quantum Dirac field on four dimensional globally hyperbolic spacetime in which the bound depends only on the local geometry; such a QWEI is known as an absolute QWEI.