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Smoothed asymptotics: from number theory to QFT

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arxiv 2401.10981 v2 pith:SRFJVJWD submitted 2024-01-19 hep-th gr-qcmath-phmath.MP

Antonio Padilla , Robert G. C. Smith This is my paper · ORCID
classification hep-thgr-qcmath-phmath.MP
keywords regularisationintegralstheoryasymptoticsconnectionfieldgaugeloop
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abstract

Inspired by the method of smoothed asymptotics developed by Terence Tao, we introduce a new ultra-violet regularisation scheme for loop integrals in quantum field theory which we call $\eta$ regularisation. This allows us to reveal a surprising 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. We also comment on a possible connection to Schwinger proper time integrals.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Nonlocal Schwinger Model

    hep-th 2024-12 accept novelty 7.0 of 10

    For 2<d<4, 2D massless fermions coupled to a d-dimensional Maxwell field are exactly described by a scalar whose scaling dimension runs from 0 in the UV to (4-d)/2 in the IR.

  2. Gauge invariance and generalised $\eta$ regularisation

    hep-th 2024-12 conditional novelty 6.0 of 10

    An extended η-regularisation formalism unifies dimensional, denominator, and Schwinger-proper-time regularisation as solutions of gauge consistency conditions, and reproduces the chiral anomaly when implemented with t...

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