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Discussing Zeta regularization techniques, this publication includes chapters on: the Reimann Zeta function; the Casimir effect in flat space-time; and properties of the chemical potential in higher-dimensional manifolds.

One of the aims of this volume is to explain in a basic manner the seemingly difficult issues of mathematical structure using some specific examples as a guide. In each of the cases considered, a comprehensible physical problem is approached, to which the corresponding mathematical scheme is applied, its usefulness being duly demonstrated. The authors try to fill the gap that always exists between the physics of quantum field theories and the mathematical methods best suited for its formulation, which are increasingly demanding on the mathematical ability of the physicist.

This volume contains discussions on group representations of SL(2,R) and automorphic forms, with applications of the Selberg trace formula to the Landau spectrum for a uniform magnetic field on a Riemann surface, on particle creation in the early universe, Chern-Simons gauge theory on 3-manifolds, path integral representation of fractional spin particles, eta and zeta functions and Dirac operators, Schrödinger operators with periodic potential, elliptic genera for SUSY sigma models, quantum fields on curved space-times, black holes, and some discussions on string theory and quantum gravity.

A collection of papers from the Londrina Workshop on Geometrical Aspects of Quantum Fields, held in Brazil in April 2000. The following topics are addressed: non-Abelian Toda models; remarks for physicists on equivariant cohomology and the Duistermaat-Heckman formula; Casimir effect; quantum groups and their application to nuclear physics; quantum field theory; quantum gravity and the theory of extended objects; and black hole physics and cosmology.