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Zeta-function regularization is a powerful method in perturbation theory. This book is meant as a guide for the student of this subject. Everything is explained in detail, in particular the mathematical difficulties and tricky points, and several applications are given to show how the procedure works in practice (e.g. Casimir effect, gravity and string theory, high-temperature phase transition, topological symmetry breaking, noncommutative spacetime). The formulas some of which are new can be used for physically meaningful, accurate numerical calculations.  The book is to be considered as a basic introduction and a collection of exercises for those who want to apply this regularization procedure in practice.   This thoroughly revised, updated and expanded edition includes in particular new explicit formulas on the general quadratic, Chowla-Selberg series case, an interplay with the Hadamard calculus, and features a new chapter on recent cosmological applications including the calculation of the vacuum energy fluctuations at large scale in braneworld and other models.

Physics --- Physical Sciences & Mathematics --- Physics - General --- Functions, Zeta. --- Mathematical physics. --- Physical mathematics --- Zeta functions --- Mathematics --- Physics. --- Quantum field theory. --- String theory. --- Mathematical Methods in Physics. --- Mathematical Physics. --- Quantum Field Theories, String Theory. --- Mathematical Applications in the Physical Sciences. --- Models, String --- String theory --- Nuclear reactions --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics