Physics, combinatorics and Hopf algebras
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| Format: | Artículo científico |
| Langue: | en |
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Sociedad Mexicana de Física A.C.
2007
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| _version_ | 1876491160886706176 |
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| author | C. Chryssomalakos |
| author_facet | C. Chryssomalakos |
| contents | Physics, combinatorics and Hopf algebras C. Chryssomalakos Física, Astronomía y Matemáticas Hopf algebras renormalization quantum measures primitive elements generalized quantum mechanics A number of problems in theoretical physics share a common nucleus of a combinatoric nature. It is argued here that Hopf algebraic conceptsand techiques can be particularly efficient in dealing with such problems. As a first example, a brief review is given of the recent work ofConnes, Kreimer and collaborators on the algebraic structure of the process of renormalization in quantum field theory. Then the concept ofk-primitive elements is introduced these are particular linear combinations of products of Feynman diagrams and it is shown, in thecontext of a toy-model, that they significantly reduce the computational cost of renormalization. As a second example, Sorkins proposal fora 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 ask-primitive elements of the Hopf algebra of functions on an appropriate infinite dimensional abelian group. 2007 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57066205 https://www.redalyc.org/journal/570/57066205/ https://www.redalyc.org/journal/570/57066205/html/ https://www.redalyc.org/journal/570/57066205/57066205.epub https://www.redalyc.org/journal/570/57066205/movil en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.2 Vol.53 |
| format | Artículo científico |
| id | redalyc_57066205 |
| institution | Redalyc |
| language | en |
| publishDate | 2007 |
| publisher | Sociedad Mexicana de Física A.C. |
| spellingShingle | Physics, combinatorics and Hopf algebras C. Chryssomalakos Física, Astronomía y Matemáticas Hopf algebras renormalization quantum measures primitive elements generalized quantum mechanics Physics, combinatorics and Hopf algebras C. Chryssomalakos Física, Astronomía y Matemáticas Hopf algebras renormalization quantum measures primitive elements generalized quantum mechanics A number of problems in theoretical physics share a common nucleus of a combinatoric nature. It is argued here that Hopf algebraic conceptsand techiques can be particularly efficient in dealing with such problems. As a first example, a brief review is given of the recent work ofConnes, Kreimer and collaborators on the algebraic structure of the process of renormalization in quantum field theory. Then the concept ofk-primitive elements is introduced these are particular linear combinations of products of Feynman diagrams and it is shown, in thecontext of a toy-model, that they significantly reduce the computational cost of renormalization. As a second example, Sorkins proposal fora 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 ask-primitive elements of the Hopf algebra of functions on an appropriate infinite dimensional abelian group. 2007 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57066205 https://www.redalyc.org/journal/570/57066205/ https://www.redalyc.org/journal/570/57066205/html/ https://www.redalyc.org/journal/570/57066205/57066205.epub https://www.redalyc.org/journal/570/57066205/movil en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.2 Vol.53 |
| title | Physics, combinatorics and Hopf algebras |
| topic | Física, Astronomía y Matemáticas Hopf algebras renormalization quantum measures primitive elements generalized quantum mechanics |
| url | https://www.redalyc.org/articulo.oa?id=57066205 https://www.redalyc.org/journal/570/57066205/ https://www.redalyc.org/journal/570/57066205/html/ https://www.redalyc.org/journal/570/57066205/57066205.epub https://www.redalyc.org/journal/570/57066205/movil |