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

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

A Unique Continuation Result for Klein-Gordon Bisolutions on a 2-dimensional Cylinder

We prove a novel unique continuation result for weak bisolutions to the massive Klein-Gordon equation on a 2-dimensional cylinder M. Namely, if such a bisolution vanishes in a neighbourhood of a `sufficiently large' portion of a 2-dimensional surface lying parallel to the diagonal in the product manifold of M with itself, then it is (globally) translationally invariant. The proof makes use of methods drawn from Beurling's theory of interpolation. An application of our result to quantum field theory on 2-dimensional cylinder spacetimes will appear elsewhere.Comment: LaTeX2e, 9 page