Zeta Regularization Techniques with Applications

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World Scientific, 1994 - 319 páginas
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.
 

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Índice

RIEMANN AND RELATED ZETA FUNCTIONS
1
ZetaRegularization of
3
ZetaFunction Regularization of Determinants
9
Uses of Zeta Function in Integration
15
ZETAFUNCTION REGULARIZATION OF SUMS OVER
23
Regularization of Double Series of the Type EpsteinHurwitz
33
Multiple Zeta Functions with Arbitrary Exponents
43
Some Remarks on the Use of the ZetaFunction Regularization
49
Path Integral Techniques and ZetaFunction Regularization of
143
Oneloop Effective Action for Scalar Fields on KaluzaKlein Space
162
References
169
Path Integral Approach for a Class of Quantum pBrane Models
183
The Casimir Energy for pBranes Compactified on Constant Curva
197
References
206
FiniteTemperature Effects with NonVanishing Chemical Potential220
220
Applications to KaluzaKlein Models
226

ZETA FUNCTION REGULARIZATION GENERALIZED
57
Applications to Effective Lagrangians for Constant Background Fields
63
Zeta Functions vs HeatKernel Regularization
70
THE CASIMIR EFFECT IN FLAT SPACETIME
79
ZetaRegularization of Lapla
107
Casimir Energy for Spherical and Cylindrical Universes
119
References
131
Free Energy for the Open Superstring Theory and Laurent Series
235
Thermodynamics of the Open Bosonic String in an External Mag
248
References
257
References
282
References
316
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