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Representations of the Renormalization Group as Matrix Lie Algebra | M. Berg
; P. Cartier
; | Date: |
31 May 2001 | Subject: | hep-th | Abstract: | Renormalization 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 | Services: | Forum | Review | PDF | Favorites |
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