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Title: Rigorous extension of the proof of zeta-function regularization
Author: Elizalde, E. (Emili), 1950-
Romeo, A.
Keywords: Teoria de camps (Física)
Funcions zeta
Field theory (Physics)
Zeta functions
Issue Date: 1989
Publisher: The American Physical Society
Abstract: The proof of $\ensuremath{\zeta}$-function regularization of high-temperature expansions, a technique which provides correct results for many field-theoretical quantities of interest, is known to fail, however, in the case of "Epstein-type" expressions such as $\ensuremath{\Sigma}{{n}_{1},\dots{},{n}_{N}=1}^{\ensuremath{\infty}}{(\ensuremath{\Sigma}{j=1}^{N}{a}_{j}{n}_{j}^{\ensuremath{\alpha}})}^{\ensuremath{-}s}$, $\ensuremath{\alpha}=2, 4, \dots{}$. After showing where precisely the existing demonstration breaks down, we provide a new proof of this regularization valid for a wider range of the parameter $\ensuremath{\alpha}$. The extra terms are calculated explicitly for any value of $\ensuremath{\alpha}\ensuremath{\le}2$. As an application, we provide the finite results corresponding to the $\ensuremath{\zeta}$-function regularization of expressions associated with field theories evaluated in partially compactified, toroidal spacetimes of the form ${\mathrm{T}}^{p}\ifmmode\times\else\texttimes\fi{}{\mathrm{R}}^{q+1}$.
Note: Reproducció digital del document publicat en format paper, proporcionada per PROLA i
It is part of: Physical Review D, 1989, vol. 40, núm, 2, p. 436-443
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ISSN: 0556-2821
Appears in Collections:Articles publicats en revistes (Física Quàntica i Astrofísica)

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