---
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.'
author:
- |
    Calvin J. Smith[^1]\
    *School of Mathematical Sciences, University College Dublin,*\
    *Belfield, Dublin 4, Ireland*
date: 15 May 2007
title: '**An absolute quantum energy inequality for the Dirac field in curved spacetime**'
---

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Introduction
============

When formulating the classical theory of general relativity it is necessary to impose certain energy conditions on the source matter fields being considered. The most commonplace of these energy conditions is the *weak energy condition*, $T_{ab}k^ak^b \geq
0$ for every timelike vector field $k$, which entails that 