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A quantum weak energy inequality for Dirac fields in curved spacetime

Fewster, C.J. and Verch, R. (2002) A quantum weak energy inequality for Dirac fields in curved spacetime. Communications in Mathematical Physics, 225 (2). pp. 331-359. ISSN 1432-0916

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Abstract

Quantum fields are well known to violate the weak energy condition of general relativity: the renormalised energy density at any given point is unbounded from below as a function of the quantum state. By contrast, for the scalar and electromagnetic fields it has been shown that weighted averages of the energy density along timelike curves satisfy “quantum weak energy inequalities” (QWEIs) which constitute lower bounds on these quantities. Previously, Dirac QWEIs have been obtained only for massless fields in two-dimensional spacetimes. In this paper we establish QWEIs for the Dirac and Majorana fields of mass m≥ 0 on general four-dimensional globally hyperbolic spacetimes, averaging along arbitrary smooth timelike curves with respect to any of a large class of smooth compactly supported positive weights. Our proof makes essential use of the microlocal characterisation of the class of Hadamard states, for which the energy density may be defined by point-splitting.

Item Type: Article
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 12 Jun 2009 09:23
Last Modified: 12 Jun 2009 09:23
Published Version: http://dx.doi.org/10.1007/s002200100584
Status: Published
Publisher: Springer Verlag
Identification Number: 10.1007/s002200100584
URI: http://eprints.whiterose.ac.uk/id/eprint/5926

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