On dimensional regularization of sums

2001/12/18 by Roberto Contino, Andrea Gambassi · 26 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Bregman divergence #Compactification (mathematics) #Dimensional regularization #Homogeneous space #Inverse problem #Quantum Electrodynamics and Casimir Effect #Regularization (linguistics) #Renormalization #Term (time) #cond-mat #hep-ph #hep-th

paper · pdf · doi:10.1063/1.1531215

published in Journal of Mathematical Physics 44(2), 570-587 (American Institute of Physics) · 22 pages, 1 figure

arxiv created 2001/12/18 · openalex publication_date 2003/01/17 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We discuss a systematic way to dimensionally regularize divergent sums arising in field theories with an arbitrary number of physical compact dimensions or finite temperature. The method preserves the same symmetries of the action as the conventional dimensional regularization and allows an easy separation of the regulated divergence from the finite term that depends on the compactification radius (temperature).

Citations

• New Developments in the Casimir Effect
• Zeta function regularization of path integrals in curved spacetime
• A note on regularization methods in Kaluza–Klein theories
• Quantum Field - Theory Models in Less Than 4 Dimensions
• Effective Lagrangian and energy-momentum tensor in de Sitter space
• Regularization and renormalization of gauge fields