Zeta function regularization for a scalar field in a compact domain

Details Zeta function regularization for a scalar field in a compact domain Zeta function regularization for a scalar field in a compact domain

2004-10-06

arxiv.org/abs/math-ph/0410019v1

J.Phys. A37 (2004) 11499-11518

Physics

Mathematical Physics

19 pages, no figures, to appear in J. Phys. A

Scientific paper

10.1088/0305-4470/37/47/018

We express the zeta function associated to the Laplacian operator on $S^1_r\times M$ in terms of the zeta function associated to the Laplacian on $M$, where $M$ is a compact connected Riemannian manifold. This gives formulas 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 to the physical models at finite temperature.

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