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.
Geometrically relating momentum cut-off and dimensional regularization
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abstract
The $\beta$ function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the $\beta$-functions of momentum cut-off regularization and dimensional regularization on scalar field theories by a gauge transformation using the Hopf algebras of the Feynman diagrams of the theories.
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Some very low-dimensional algebraic topology
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.