IntegrableN-dimensional systems on the Hopf algebra andq-deformations; Theoretical and Mathematical Physics; Vol. 124, iss. 3
| Parent link: | Theoretical and Mathematical Physics: Scientific Journal Vol. 124, iss. 3.— 2000.— [P. 1172-1186] |
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| Sammanfattning: | Title screen We construct the class of integrable classical and quantum systems on the Hopf algebras describing n interacting particles. We obtain the general structure of an integrable Hamiltonian system for the Hopf algebra A(g) of a simple Lie algebra g and prove that the integrals of motion depend only on linear combinations of k coordinates of the phase space, 2·ind g≤k≤g·ind g, whereind g andg are the respective index and Coxeter number of the Lie algebra g. The standard procedure of q-deformation results in the quantum integrable system. We apply this general scheme to the algebras sl(2), sl(3), and o(3, 1). An exact solution for the quantum analogue of the N-dimensional Hamiltonian system on the Hopf algebra A(sl(2)) is constructed using the method of noncommutative integration of linear differential equations Режим доступа: по договору с организацией-держателем ресурса |
| Språk: | engelska |
| Publicerad: |
2000
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| Länkar: | http://link.springer.com/article/10.1007%2FBF02550996 |
| Materialtyp: | Elektronisk Bokavsnitt |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=636555 |
| Sammanfattning: | Title screen We construct the class of integrable classical and quantum systems on the Hopf algebras describing n interacting particles. We obtain the general structure of an integrable Hamiltonian system for the Hopf algebra A(g) of a simple Lie algebra g and prove that the integrals of motion depend only on linear combinations of k coordinates of the phase space, 2·ind g≤k≤g·ind g, whereind g andg are the respective index and Coxeter number of the Lie algebra g. The standard procedure of q-deformation results in the quantum integrable system. We apply this general scheme to the algebras sl(2), sl(3), and o(3, 1). An exact solution for the quantum analogue of the N-dimensional Hamiltonian system on the Hopf algebra A(sl(2)) is constructed using the method of noncommutative integration of linear differential equations Режим доступа: по договору с организацией-держателем ресурса |
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