1 research outputs found
Zeta function regularization for a scalar field in a compact domain
We express the zeta function associated to the Laplacian operator on
in terms of the zeta function associated to the Laplacian on
, where 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 . Furthermore, we provide an exact
formula for the zeta function at any value of when is a -dimensional
box or a -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.Comment: 19 pages, no figures, to appear in J. Phys.