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Quantum energy inequalities in two-dimensional conformal field theory

Fewster, C.J. and Hollands, S. (2005) Quantum energy inequalities in two-dimensional conformal field theory. Reviews in Mathematical Physics, 17 (5). pp. 577-612. ISSN 0129-055X

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Abstract

Quantum energy inequalities (QEIs) are state-independent lower bounds on weighted averages of the stress-energy tensor, and have been established for several free quantum field models. We present rigorous QEI bounds for a class of interacting quantum fields, namely the unitary, positive energy conformal field theories (with stress-energy tensor) on two-dimensional Minkowski space. The QEI bound depends on the weight used to average the stress-energy tensor and the central charge(s) of the theory, but not on the quantum state. We give bounds for various situations: averaging along timelike, null and spacelike curves, as well as over a space-time volume. In addition, we consider boundary conformal field theories and more general "moving mirror" models.

Our results hold for all theories obeying a minimal set of axioms which — as we show — are satisfied by all models built from unitary highest-weight representations of the Virasoro algebra. In particular, this includes all (unitary, positive energy) minimal models and rational conformal field theories. Our discussion of this issue collects together (and, in places, corrects) various results from the literature which do not appear to have been assembled in this form elsewhere.

Item Type: Article
Keywords: Quantum field theory; energy inequalities; conformal field theory
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 12 Feb 2009 17:55
Last Modified: 12 Feb 2009 17:55
Published Version: http://dx.doi.org/10.1142/S0129055X05002406
Status: Published
Publisher: World Scientific Publishing
Identification Number: 10.1142/S0129055X05002406
URI: http://eprints.whiterose.ac.uk/id/eprint/7469

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