Representations of the Renormalization Group as Matrix Lie Algebra
| dc.creator | Berg, M. | |
| dc.creator | Cartier, P. | |
| dc.date | 2001-05-31 | |
| dc.date | 2004-02-14 | |
| dc.date.accessioned | 2026-07-07T04:11:44Z | |
| dc.date.available | 2026-07-07T04:11:44Z | |
| dc.description | 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. | |
| dc.description | 32 pages, uses feynmf package. v2: added appendix, corrected typos | |
| dc.identifier | https://arxiv.org/abs/hep-th/0105315 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0105315 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/50710 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Representations of the Renormalization Group as Matrix Lie Algebra | |
| dc.type | text |