Zeta Regularization Techniques with Applications

Front Cover
World Scientific, 1994 - Science - 319 pages
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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Contents

ZetaRegularization of
3
Riemann and Hurwitz Zeta Functions
4
References
20
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
ZETA FUNCTION REGULARIZATION GENERALIZED
57
Applications to Effective Lagrangians for Constant Background Fields
63
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 Potential
220
Applications to KaluzaKlein Models
226
Free Energy for the Open Superstring Theory and Laurent Series
235

Zeta Functions vs HeatKernel Regularization
70
References
78
Energy
84
ZetaRegularization of Lapla
107
Casimir Energy for Spherical and Cylindrical Universes
119
References
131
Path Integral Techniques and ZetaFunction Regularization of
143
Thermodynamics of the Open Bosonic String in an External Mag
248
References
257
The OneLoop Effective Action for 2D Induced Gravity on a Com
263
References
282
The SeeleyGilkey Coefficients
288
References
316
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