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The geometric $\beta$-function in curved space-time under operator regularization

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arxiv 0909.4122 v3 pith:XCEKQ46P submitted 2009-09-23 math-ph math.MP

Susama Agarwala This is my paper · ORCID
classification math-phmath.MP
keywords betageometricfunctionregularizationanalysisdefinedextendflow
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abstract

In this paper, I compare the generators of the renormalization group flow, or the geometric $\beta$-functions for dimensional regularization and operator regularization. I then extend the analysis to show that the geometric $\beta$-function for a scalar field theory on a closed compact Riemannian manifold is defined on the entire manifold. I then extend the analysis to find the generator of the renormalization group flow for a conformal scalar-field theories on the same manifolds. The geometric $\beta$-function in this case is not defined.

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  1. Some very low-dimensional algebraic topology

    math.AT 2024-11 unverdicted novelty 4.0 of 10

    Proposes that the group completion of planar configuration spaces, equivalent to ΩS^2, is a moduli space whose Jordan-curve states encode renormalized Feynman integrals as residues.

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