%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 }