Zeta-Function Regularization, the Multiplicative Anomaly and the Wodzicki Residue

1997/01/31 by E. Elizalde, Luciano Vanzo, L. Vanzo +2 · 1 citation
Chemistry · Mathematics · Medicine · Physics and Astronomy · #Advanced Operator Algebra Research #Arithmetic zeta function #Artificial intelligence #Biochemistry #Chemistry #Computer science #Mathematical analysis #Mathematics #Medicine #Multiplicative function #Prime zeta function #Pure mathematics #Quantum Electrodynamics and Casimir Effect #Quantum and Classical Electrodynamics #Regularization (linguistics) #Residue (chemistry) #Riemann zeta function #Zeta function regularization #hep-th

paper · pdf · doi:10.1007/s002200050371

published as Commun.Math.Phys. 194 (1998) 613-630 · LaTeX, 17 pages, 3 figures. Small corrections, two new formulas, and an addition to the references. To appear in Commun. Math. Phys

arxiv created 1997/11/07 · openalex publication_date 1998/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The multiplicative anomaly associated with the zeta-function regularized determinant is computed for the Laplace-type operators L₁=-\lap+V₁ and L₂=-\lap+V₂, with V₁, V₂ constant, in a D-dimensional compact smooth manifold M_D, making use of several results due to Wodzicki and by direct calculations in some explicit examples. It is found that the multiplicative anomaly is vanishing for D odd and for D=2. An application to the one-loop effective potential of the O(2) self-interacting scalar model is outlined.

Citations

• The Standard Model as a noncommutative geometry: the low-energy regime
• On the universal Chamseddine–Connes action. I. Details of the action computation

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