Andrei A Bytsenko – författare

This book is the result of several years of work by the authors on different aspects of zeta functions and related topics. The aim is twofold. On one hand, a considerable number of useful formulas, essential for dealing with the different aspects of zeta-function regularization (analytic continuation, asymptotic expansions), many of which appear here, in book format, for the first time are presented. On the other hand, the authors show explicitly how to make use of such formulas and techniques in practical applications to physical problems of very different nature. Virtually all types of zeta functions are dealt with in the book.

One of the aims of this book 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.