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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.
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ZetaRegularization of. ZetaFunction Regularization of Determinants.
Ten Physical Applications of Spectral Zeta Functions
Uses of Zeta Function in Integration. Multiple Zeta Functions with Arbitrary Exponents.
Applications to KaluzaKlein Models. Zeta Functions vs HeatKernel Regularization. ZetaRegularization of Lapla. Casimir Energy for Spherical and Cylindrical Universes.
Download Ten Physical Applications Of Spectral Zeta Functions
Dowker Laplacian Lett limit manifold Math Mellin transform meromorphic method metric Nucl obtained one-loop operator p-brane parameter partition function Phys pole potential quadratic quantization quantum field Quantum Grav renormalization residue result Riemann spheres Riemann zeta function S. Odintsov scalar field Selberg trace formula semicircumference space spacetime spinor string theory subsection summation supermembrane taking theorem topology vacuum energy vanish Witt zero modes zeta function regularization zeta-function regularization.
Magnus, F. Those properties are certainly to be counted among their main virtues, but oddly enough in some sense also as its drawbacks: we do not manage to see clearly how and what infinites are thrown away, something that is evident in other more pedestrian regularizations which are actually equivalent in some cases to the zeta one, as pointed out, 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.