Elizalde, E. (2013) Chowla-Selberg series and other formulas useful in zeta regularization. Il nuovo cimento C, 36 (3). pp. 95-106. ISSN 1826-9885
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Abstract
The role of the Riemann zeta function as a regularization tool is briefly review and a general scheme for the physically relevant quadratic and linear cases is discussed. The use and importance of the Chowla-Selberg series formula, together with its non-trivial extensions, to deal with situations where the spectrum is known explicitly is stressed. The derivation of such formulas is shown to rely on other fundamental expressions of mathematics, as the Poisson summation formula and Jacobi’s theta function identity. Their uses in the zeta regularization of infinite quantities in quantum field theory is sketched. The second part of the paper addresses operator zeta functions, regularized traces and residues, and the multiplicative anomaly or defect of the determinant, together with potential applications.
| Item Type: | Article |
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| Uncontrolled Keywords: | Sequences, series, and summability ; Renormalization ; Special functions ; Operator theory |
| Subjects: | 500 Scienze naturali e Matematica > 530 Fisica |
| Depositing User: | Marina Spanti |
| Date Deposited: | 05 May 2020 12:51 |
| Last Modified: | 05 May 2020 12:51 |
| URI: | http://eprints.bice.rm.cnr.it/id/eprint/18270 |
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