Functional Determinant of the Massive Laplace Operator and the Multiplicative Anomaly

Abstract

After a brief survey of zeta function regularization issues and of the related multiplicative anomaly, illustrated with a couple of basic examples, namely the harmonic oscillator and quantum field theory at finite temperature, an application of these methods to the computation of functional determinants corresponding to massive Laplacians on spheres in arbitrary dimensions is presented. Explicit formulas are provided for the Laplace operator on spheres in $N=1,2,3,4$ dimensions and for `vector' and `tensor' Laplacians on the unitary sphere $S^4$.

arXiv comment15 pages, LaTex

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• Notes on peculiarities of Schwinger--DeWitt technique: one-loop double poles, total-derivative terms and determinant anomalies
• Effective action for conformal spins on spheres with the multiplicative and conformal anomalies
• Gelfand-Yaglom formula for functional determinants in higher dimensions
• Massive scalar Casimir interaction beyond proximity force approximation