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Angles, Scales and Parametric Renormalization

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Abstract

We discuss the structure of renormalized Feynman rules. Regarding them as maps from the Hopf algebra of Feynman graphs to \({\mathbb{C}}\) originating from the evaluation of graphs by Feynman rules, they are elements of a group \({G=\mathrm{Spec}_{\mathrm{Feyn}}(H)}\) . We study the kinematics of scale and angle-dependence to decompose G into subgroups \({G_{\mathrm{\makebox{1-s}}}}\) and \({G_{\mathrm{fin}}}\) . Using parametric representations of Feynman integrals, renormalizability and the renormalization group underlying the scale dependence of Feynman amplitudes are derived and proven in the context of algebraic geometry.

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Authors and Affiliations

  1. Institut des Hautes Etudes Scientifiques, 35, route de Chartres, 91440, Bures-sur-Yvette, France

    Francis Brown

  2. Humboldt University, Unter den Linden 6, 10099, Berlin, Germany

    Dirk Kreimer

Authors
  1. Francis Brown
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  2. Dirk Kreimer
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Corresponding author

Correspondence to Dirk Kreimer.

Additional information

F. Brown was supported by CNRS and ERC grant 257638.

D. Kreimer, Alexander von Humboldt Chair in Mathematical Physics, was supported by the Alexander von Humboldt Foundation and the BMBF.

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Brown, F., Kreimer, D. Angles, Scales and Parametric Renormalization. Lett Math Phys 103, 933–1007 (2013). https://doi.org/10.1007/s11005-013-0625-6

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  • DOI: https://doi.org/10.1007/s11005-013-0625-6

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