Physics, Combinatorics and Hopf Algebras
| dc.creator | Chryssomalakos, Chryssomalis | |
| dc.date | 2004-08-21 | |
| dc.date.accessioned | 2026-07-07T04:17:21Z | |
| dc.date.available | 2026-07-07T04:17:21Z | |
| dc.description | A number of problems in theoretical physics share a common nucleus of combinatoric nature. It is argued here that Hopf algebraic concepts and techiques can be particularly efficient in dealing with such problems. As a first example, a brief review is given of the recent work of Connes, Kreimer and collaborators on the algebraic structure of the process of renormalization in quantum field theory. Then the concept of $k$-primitive elements is introduced -- these are particular linear combinations of products of Feynman diagrams -- and it is shown, in the context of a toy-model, that they significantly reduce the computational cost of renormalization. As a second example, Sorkin's proposal for a family of generalizations of quantum mechanics, indexed by an integer $k>2$, is reviewed (classical mechanics corresponds to $k=1$, while quantum mechanics to $k=2$). It is then shown that the quantum measures of order $k$ proposed by Sorkin can also be described as $k$-primitive elements of the Hopf algebra of functions on an appropriate infinite dimensional abelian group. | |
| dc.description | 16 pages. Invited talk given at the V Workshop of the DGFM of the Mexican Physical Society, Morelia, Mexico, November 2003. Also presented in the conference ``Non-Commutative Geometry and Representation Theory in Mathematical Physics'', held in Karlstad, Sweeden in July 2004, and elsewhere | |
| dc.identifier | https://arxiv.org/abs/hep-th/0408165 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0408165 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/52720 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Physics, Combinatorics and Hopf Algebras | |
| dc.type | text |