Elliptic functions and temperature inversion symmetry on spheres

Abstract

Finite temperature boson and fermion field theories on ultrastatic space-times with a d-sphere spatial section 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 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.

33 pages, JyTeX

Cited by in corpus (8)

• Partition Functions, the Bekenstein Bound and Temperature Inversion in Anti-de Sitter Space and its Conformal Boundary
• Zero modes, entropy bounds and partition functions
• Elliptic Thermal Correlation Functions and Modular Forms in a Globally Conformal Invariant QFT
• Conformal invariance and rationality in an even dimensional quantum field theory
• Generalized Schlömilch's formulas and thermal Casimir effect of a fermionic rectangular box
• Quantum revivals in free field CFT
• Ambiguities in the local thermal behavior of the scalar radiation in one-dimensional boxes
• Elliptic aspects of statistical mechanics on spheres