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25 April 2024
 
  » arxiv » hep-th/0105315

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Representations of the Renormalization Group as Matrix Lie Algebra
M. Berg ; P. Cartier ;
Date 31 May 2001
Subject hep-th
AbstractRenormalization is cast in the form of a Lie algebra of infinite triangular matrices. By exponentiation, these matrices generate counterterms for Feynman diagrams with subdivergences. As representations of an insertion operator, the matrices are related to the Connes-Kreimer Lie algebra. In fact, the right-symmetric nonassociative algebra of the Connes-Kreimer insertion product is equivalent to an "Ihara bracket" in the matrix Lie algebra. We check our results in a three-loop example in scalar field theory. Apart from possible applications in high-precision phenomenology, we give a few ideas about possible applications in noncommutative geometry and functional integration.
Source arXiv, hep-th/0105315
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