Mathematical Physics


Summary of the Zeta Regularization Method Applied to the Calculation of Divergent Series and Divergent Integrals

Authors: Jose Javier Garcia Moreta

•ABSTRACT: We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals for positive ‘s’ , using the Euler Maclaurin summation formula, we manage to express a divergent integral in term of a linear combination of divergent series , these series can be regularized using the Riemann Zeta function s >0 , in the case of the pole at s=1 we use a property of the Functional determinant to obtain the regularization , with the aid of the Laurent series in one and several variables we can extend zeta regularization to the cases of integrals , we believe this method can be of interest in the regularization of the divergent UV integrals in Quantum Field theory since our method would not have the problems of the Analytic regularization or dimensional regularization •Keywords: = Riemann Zeta function, Functional determinant, Zeta regularization, divergent series .

Comments: 20 Pages.

Download: PDF

Submission history

[v1] 13 Sep 2010
[v2] 8 Nov 2010
[v3] 11 Feb 2011
[v4] 23 Feb 2011
[v5] 2013-05-03 15:35:33

Unique-IP document downloads: 769 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus