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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
55/2002

Elliptic functions and temperature inversion symmetry on spheres

J. Stuart Dowker and Klaus Kirsten

Abstract

Finite temperature boson and fermion free field theories on the space-time manifolds $\oR\times$S$^d$ are discussed with one eye on the questions of temperature inversion symmetry and modular invariance. For conformally invariant theories it is shown that the total energy at any temperature for any odd dimension, $d$, is given as a power series in the $d=3$ and $d=5$ energies, for scalars, and the $d=1$ and $d=3$ energies for spinors. Further, these energies can be given in finite terms at specific temperatures associated with singular moduli of elliptic function theory. Some examples are listed and numbers given.

Received:
11.07.02
Published:
11.07.02
MSC Codes:
33E05
PACS:
11.10.Wx
Keywords:
elliptic functions, finite temperature, inversion symmetry

Related publications

inJournal
2002 Repository Open Access
J. Stewart Dowker and Klaus Kirsten

Elliptic functions and temperature inversion symmetry on spheres

In: Nuclear physics / B, 638 (2002) 3, pp. 405-432