Green functions and dimensional reduction of quantum fields on product manifolds
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Publication:5458961
DOI10.1088/0264-9381/25/7/075005zbMATH Open1147.83018arXiv0709.3227OpenAlexW1971471150MaRDI QIDQ5458961
Publication date: 24 April 2008
Published in: Classical and Quantum Gravity (Search for Journal in Brave)
Abstract: We discuss Euclidean Green functions on product manifolds P=NxM. We show that if M is compact then the Euclidean field on P can be approximated by its zero mode which is a Euclidean field on N. We estimate the remainder of this approximation. We show that for large distances on N the remainder is small. If P=R^{D-1}xS^{beta}, where S^{beta} is a circle of radius beta, then the result reduces to the well-known approximation of the D dimensional finite temperature quantum field theory to D-1 dimensional one in the high temperature limit. Analytic continuation of Euclidean fields is discussed briefly.
Full work available at URL: https://arxiv.org/abs/0709.3227
Methods of quantum field theory in general relativity and gravitational theory (83C47) Kaluza-Klein and other higher-dimensional theories (83E15)
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