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Finite temperature field theory on the Moyal plane

By Earnest Akofor and Aiyalan P. Balachandran

Abstract

10 pages, no figures.-- PACS nr.: 11.10.Wx.-- ArXiv pre-print available at: http://arxiv.org/abs/0907.0905v1.pdfIn this paper, we initiate the study of finite temperature quantum field theories on the Moyal plane. Such theories violate causality which influences the properties of these theories. In particular, causality influences the fluctuation-dissipation theorem: as we show, a disturbance in a space-time region M1 creates a response in a space-time region M2 spacelike with respect to M1 (M1×M2). The relativistic Kubo formula with and without noncommutativity is discussed in detail, and the modified properties of relaxation time and the dependence of mean square fluctuations on time are derived. In particular, the Sinha-Sorkin result [Phys. Rev. B 45, 8123 (1992)] on the logarithmic time dependence of the mean square fluctuations is discussed in our context. We derive an exact formula for the noncommutative susceptibility in terms of the susceptibility for the corresponding commutative case. It shows that noncommutative corrections in the four-momentum space have remarkable periodicity properties as a function of the four-momentum k. They have direction dependence as well and vanish for certain directions of the spatial momentum. These are striking observable signals for noncommutativity. The Lehmann representation is also generalized to any value of the noncommutativity parameter θ(μν) and finite temperatures.This work was supported by the US Department of Energy under grant number DE-FG02-85ER40231 and by the Universidad Carlos III de Madrid.Publicad

Topics: [PACS] Finite-temperature field theory, Matemáticas
Publisher: 'American Physical Society (APS)'
Year: 2009
DOI identifier: 10.1103/PhysRevD.80.036008
OAI identifier: oai:e-archivo.uc3m.es:10016/6936

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