2023/09/08 by Rodrigo Aros, Aros, R., F. Bugini +5 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2309.04471
openalex publication_date 2023/09/08 · openalex created_date 2023/09/12 · openalex updated_date 2026/07/28
An explicit formula to compute the multiplicative anomaly or defect of ζ-regularized products of linear factors is derived, by using a Feynman parametrization, generalizing Shintani-Mizuno formulas. Firstly, this is applied on n-spheres, reproducing known results in the literature. Then, this framework is applied to a closed Einstein universe at finite temperature, namely S1β× Sn-1. In doing so, it is shown that the standard Casimir energy for GJMS operators coincides with the accumulated multiplicative anomaly for the shifted Laplacians that build them up. This equivalence between Casimir energy and multiplicative anomaly, unnoticed so far to our knowledge, brings about a new turn regarding the physical significance of the multiplicative anomaly, putting both now on equal footing. An emergent improved Casimir energy, that takes into account the multiplicative anomaly among the building Laplacians, is also discussed.