Smoothed asymptotics: from number theory to QFT

Padilla, Antonio; Smith, Robert G. C.

Abstract

Inspired by the method of smoothed asymptotics developed by Terence Tao, we introduce a new ultraviolet regularisation scheme for loop integrals in quantum field theory which we call η regularisation. This reveals a connection between the elimination of divergences in divergent series of powers and the preservation of gauge invariance in the regularisation of loop integrals in quantum field theory. In particular , we note that a method for regularising the series of natural numbers so that it converges to minus one twelfth inspires a regularisation scheme for non-abelian gauge theories coupled to Dirac fermions that preserves the Ward identity for the vacuum polarisation tensor and other higher point functions. We also comment on a possible connection to Schwinger proper time integrals.

Citation

Padilla, A., & Smith, R. G. (2024). Smoothed asymptotics: from number theory to QFT. Physical Review D, 110(2), Article 025010. https://doi.org/10.1103/PhysRevD.110.025010

• Journal Article Type: Article
• Acceptance Date: Jun 10, 2024
• Online Publication Date: Jul 15, 2024
• Publication Date: Jul 15, 2024
• Deposit Date: Jun 20, 2024
• Publicly Available Date: Jul 15, 2024
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 110
• Issue: 2
• Article Number: 025010
• DOI: https://doi.org/10.1103/PhysRevD.110.025010
• Public URL: https://nottingham-repository.worktribe.com/output/36299977
• Publisher URL: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.110.025010