Zeta function regularization for a scalar field in a compact domain
G. Ortenzi, and M. Spreafico. Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
We express the zeta function associated with the Laplacian operator on $S^1_r M$ in terms of the zeta function associated with the Laplacian on $M$, where $M$ is a compact connected Riemannian manifold. This gives formulae for the partition function of the associated physical model at low and high temperature for any compact domain $M$. Furthermore, we provide an exact formula for the zeta function at any value of $r$ when $M$ is a $D$--dimensional box or a $D$--dimensional torus; this allows a rigorous calculation of the zeta invariants and the analysis of the main thermodynamic functions associated with the physical models at finite temperature.
%0 Book Section
%1 statphys23_1066
%A Ortenzi, G.
%A Spreafico, M.
%B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics
%C Genova, Italy
%D 2007
%E Pietronero, Luciano
%E Loreto, Vittorio
%E Zapperi, Stefano
%K boson casimir effect gas statphys23 topic-1
%T Zeta function regularization for a scalar field in a compact domain
%U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1066
%X We express the zeta function associated with the Laplacian operator on $S^1_r M$ in terms of the zeta function associated with the Laplacian on $M$, where $M$ is a compact connected Riemannian manifold. This gives formulae for the partition function of the associated physical model at low and high temperature for any compact domain $M$. Furthermore, we provide an exact formula for the zeta function at any value of $r$ when $M$ is a $D$--dimensional box or a $D$--dimensional torus; this allows a rigorous calculation of the zeta invariants and the analysis of the main thermodynamic functions associated with the physical models at finite temperature.
@incollection{statphys23_1066,
abstract = {We express the zeta function associated with the Laplacian operator on ${S^1}_r \times M$ in terms of the zeta function associated with the Laplacian on $M$, where $M$ is a compact connected Riemannian manifold. This gives formulae for the partition function of the associated physical model at low and high temperature for any compact domain $M$. Furthermore, we provide an exact formula for the zeta function at any value of $r$ when $M$ is a $D$--dimensional box or a $D$--dimensional torus; this allows a rigorous calculation of the zeta invariants and the analysis of the main thermodynamic functions associated with the physical models at finite temperature.},
added-at = {2007-06-20T10:16:09.000+0200},
address = {Genova, Italy},
author = {Ortenzi, G. and Spreafico, M.},
biburl = {https://www.bibsonomy.org/bibtex/20aea37ffaa89290e529db4058223776f/statphys23},
booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano},
interhash = {7cec2cc323a05f05e5e3e9e674878eb2},
intrahash = {0aea37ffaa89290e529db4058223776f},
keywords = {boson casimir effect gas statphys23 topic-1},
month = {9-13 July},
timestamp = {2007-06-20T10:16:38.000+0200},
title = {Zeta function regularization for a scalar field in a compact domain},
url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1066},
year = 2007
}