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Miscellaneous Applications Combining Zeta with Other Regularization Procedures

  • Emilio Elizalde
Part of the Lecture Notes in Physics book series (LNP, volume 855)

Abstract

In this chapter the following applications of the method of zeta-function regularization are described. Firstly, some aspects of the comparison that was established by Fujikawa between the generalized Pauli–Villars regularization method and of the covariant regularization of composite current operators are investigated. Secondly, a calculation of the Casimir energy for the transverse oscillations of a piecewise uniform closed string is performed in detail. The string consists of two parts, each having in general different tension and mass density, but adjusted in such a way that the velocity of sound always equals the velocity of light. This model was introduced by I. Brevik and H.B. Nielsen. For the calculation, an interesting modification of the zeta function method as described up to now needs be performed, in the sense that it must be combined with some basic theorems of complex analysis (as the Cauchy or argument theorems). Also, a comparison with the results obtained by means of the introduction of a cut-off will be established which provides additional physical insight to the zeta function procedure. Hadamard regularization is also discussed, as a very useful auxiliary tool to the zeta method, in dealing with additional infinities and physical cut-offs. This aspect of comparing zeta-function’s analytic continuation with other regularization procedures is the main point in common in the examples studied here.

Keywords

Zeta Function Casimir Force Casimir Energy Dispersion Function Transverse Oscillation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of Space ScienceHigher Council for Scientific ResearchBellaterra (Barcelona)Spain

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