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Quantum Weak Energy Inequalities for the Dirac field in Flat Spacetime
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.Comment: 8 pages, REVTeX4, version to appear in Phys Rev
Energy Inequalities in Quantum Field Theory
Quantum fields are known to violate all the pointwise energy conditions of
classical general relativity. We review the subject of quantum energy
inequalities: lower bounds satisfied by weighted averages of the stress-energy
tensor, which may be regarded as the vestiges of the classical energy
conditions after quantisation. Contact is also made with thermodynamics and
related issues in quantum mechanics, where such inequalities find analogues in
sharp Gaarding inequalities.Comment: 13pp. Expanded and updated version of a contribution to the
proceedings of the XIV ICMP, Lisbon 200
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