Thermodynamics, Euclidean gravity and Kaluza-Klein reduction

Citation
Dv. Fursaev et A. Zelnikov, Thermodynamics, Euclidean gravity and Kaluza-Klein reduction, CLASS QUANT, 18(18), 2001, pp. 3825-3842
Citations number
21
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
CLASSICAL AND QUANTUM GRAVITY
ISSN journal
0264-9381 → ACNP
Volume
18
Issue
18
Year of publication
2001
Pages
3825 - 3842
Database
ISI
SICI code
0264-9381(20010921)18:18<3825:TEGAKR>2.0.ZU;2-Z
Abstract
The aim of this paper is to find a correspondence between the one-loop effe ctive action W-E defined by means of a path integral in Euclidean gravity a nd the free energy F obtained by summation over the modes. The analysis is given for quantum fields on stationary spacetimes of a general form. For su ch problems a convenient procedure of a 'Wick rotation' from Euclidean to L orentzian theory becomes quite non-trivial, implying transition from one re al section of a complexified spacetime manifold to another. We formulate co nditions under which F and W-E can be connected and establish an explicit r elation of these functionals. Our results are based on the Kaluza-Klein met hod which enables one to reduce the problem on a stationary spacetime to an equivalent problem on a static spacetime in the presence of a gauge connec tion. As a byproduct, we discover a relation between the asymptotic heat-ke rnel coefficients of elliptic operators on a D-dimensional stationary space times and the heat kernel coefficients of (D - 1)-dimensional elliptic oper ators with an Abelian gauge connection.