Corpus ID: 119285004

Dynkin operators, renormalization and the geometric $\beta$ function

  title={Dynkin operators, renormalization and the geometric \$\beta\$ function},
  author={Susama Agarwala},
  journal={arXiv: Mathematical Physics},
  • Susama Agarwala
  • Published 2012
  • Physics, Mathematics
  • arXiv: Mathematical Physics
  • In this paper, I show a close connection between renormalization and a generalization of the Dynkin operator in terms of logarithmic derivations. The geometric $\beta$ function, which describes the dependence of a Quantum Field Theory on an energy scale defines is defined by a complete vector field on a Lie group $G$ defined by a QFT. It also defines a generalized Dynkin operator. 


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    Anatomy of a gauge theory
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    Renormalization of Gauge Fields: A Hopf Algebra Approach
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    The geometric $\beta$-function in curved space-time under operator regularization
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    Logarithmic derivatives and generalized Dynkin operators
    • 8
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    A Lie Theoretic Approach to Renormalization
    • 64
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    • 17
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    Renormalization in quantum field theory and the Riemann- Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
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