2001/05/31 by M. Berg, Marcus Berg, Berg, M. +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Affine Lie algebra #Algebra over a field #Algebraic structures and combinatorial models #Current algebra #FOS: Physical sciences #Geometry #Graded Lie algebra #High Energy Physics - Theory (hep-th) #Lie algebra #Lie conformal algebra #Lie group #Mathematics #Pure mathematics #Scalar (mathematics) #Universal enveloping algebra #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0105315
32 pages, uses feynmf package. v2: added appendix, corrected typos
openalex publication_date 2001/05/31 · arxiv created 2004/02/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.