Stressenergy tensor correlators of a quantum field in Euclidean R^{N} and AdS^{N} spaces via the generalized zetafunction method
Abstract
In this paper we calculate the vacuum expectation values of the stressenergy bitensor of a massive quantum scalar field with general coupling to Ndimensional Euclidean spaces and hyperbolic spaces which are Euclidean sections of the antide Sitter spaces. These correlators, also known as the noise kernel, act as sources in the EinsteinLangevin equations of stochastic gravity [B. L. Hu and E. Verdaguer, Living Rev. Relativity14338351 11, 3 (2008).][B. L. Hu and E. Verdaguer, Classical Quantum GravityCQGRDG02649381 20, R1 (2003).10.1088/02649381/20/6/201] which govern the induced metric fluctuations beyond the meanfield dynamics described by the semiclassical Einstein equations of semiclassical gravity. Because these spaces are maximally symmetric the eigenmodes have analytic expressions which facilitate the computation of the zeta function [J. S. Dowker and R. Critchley, Phys. Rev. DPRVDAQ05562821 13, 224 (1976); 10.1103/PhysRevD.13.224J. S. DowkerR. Critchley, Phys. Rev. DPRVDAQ05562821 13, 3224 (1976).10.1103/PhysRevD.13.3224][S. W. Hawking, Commun. Math. Phys. 55, 133 (1977).CMPHAY0010361610.1007/BF01626516]. Upon taking the second functional variation of the generalized zeta function introduced in [N. G. Phillips and B. L. Hu, Phys. Rev. DPRVDAQ05562821 55, 6123 (1997).10.1103/PhysRevD.55.6123] we obtain the correlators of the stress tensor for these two classes of spacetimes. Both the short and the large geodesic distance limits of the correlators are presented for dimensions up to 11. We mention current research problems in early universe cosmology, black hole physics and gravityfluid duality where these results can be usefully applied to.
 Publication:

Physical Review D
 Pub Date:
 August 2011
 DOI:
 10.1103/PhysRevD.84.044032
 arXiv:
 arXiv:1105.5308
 Bibcode:
 2011PhRvD..84d4032C
 Keywords:

 04.62.+v;
 05.40.a;
 11.10.Kk;
 Quantum field theory in curved spacetime;
 Fluctuation phenomena random processes noise and Brownian motion;
 Field theories in dimensions other than four;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 RevTeX, 35 pages, no figure