Ten Physical Applications of Spectral Zeta FunctionsThis monography is, in the first place, a commented guide that invites the reader to plunge into the thrilling world ofzeta functions and their appli cations in physics. Different aspects ofthis field ofknowledge are considered, as one can see specifically in the Table of Contents. The level of the book is elementary. It is intended for people with no or little knowledge of the subject. Everything is explained in full detail, in particular, the mathematical difficulties and tricky points, which too often constitute an insurmountable barrier for those who would have liked to be come aquainted with that matter but never dared to ask (or did not manage to understand more complete, higher-level treatises). In this sense the present work is to be considered as a basic introduction and exercise collection for other books that have appeared recently. Concerning the physical applications of the method ofzeta-function reg ularization here described, quite a big choice is presented. The reader must be warned, however, that I have not tried to explain the underlying physi cal theories in complete detail (since this is undoubtedly out of scope), but rather to illustrate - simply and clearly - the precise way the method must be applied. Sometimes zeta regularization is explicitly compared in the text with other procedures the reader is supposed to be more familiar with (such as cut-off or dimensional regularization). |
Contents
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a₁ analytical continuation arbitrary asymptotic expansion asymptotic series behavior Bessel functions boundary conditions calculation Casimir effect Casimir energy Chapt complex plane consider contour contribution convergent corresponding defined derivative differential operator dimensional dimensions Dirichlet effective potential eigenvalues Elizalde Epstein zeta functions Epstein-Hurwitz equation explicit explicitly expression formula given heat-kernel Hurwitz zeta function infinite inhomogeneous integral k₁ L₁ Lett massless scalar field Math mathematical Mellin transform method ms+1 Nucl numerical obtain one-loop p-brane parameter particular Phys physical applications plates pole quadratic quantum field theory regularization theorem renormalization result Riemann zeta function semicircumference at infinity simple spacetime string summation symmetry breaking techniques topologically generated mass vacuum energy vacuum energy density values w₁ Waals forces zero zeta function regularization zeta-function regularization procedure