| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Int Ctr Condensed Matter Phys, BR-70919970 Brasilia, DF - Brazil
[2] Univ Sao Paulo, Inst Fis, BR-05315970 Sao Paulo - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | Journal of Mathematical Physics; v. 50, n. 10 OCT 2009. |
| Web of Science Citations: | 10 |
| Abstract | |
We investigate the quantum integrability of the Landau-Lifshitz (LL) model and solve the long-standing problem of finding the local quantum Hamiltonian for the arbitrary n-particle sector. The particular difficulty of the LL model quantization, which arises due to the ill-defined operator product, is dealt with by simultaneously regularizing the operator product and constructing the self-adjoint extensions of a very particular structure. The diagonalizibility difficulties of the Hamiltonian of the LL model, due to the highly singular nature of the quantum-mechanical Hamiltonian, are also resolved in our method for the arbitrary n-particle sector. We explicitly demonstrate the consistency of our construction with the quantum inverse scattering method due to Sklyanin {[}Lett. Math. Phys. 15, 357 (1988)] and give a prescription to systematically construct the general solution, which explains and generalizes the puzzling results of Sklyanin for the particular two-particle sector case. Moreover, we demonstrate the S-matrix factorization and show that it is a consequence of the discontinuity conditions on the functions involved in the construction of the self-adjoint extensions. (AU) | |
| FAPESP's process: | 05/05147-3 - Integrable structure of the string theory |
| Grantee: | Arsen Melikyan |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 06/56056-0 - Methods and applications of noncommutative geometry: twisted symmetry and quantum gravity |
| Grantee: | Aleksandr Nikolaievich Pinzul |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |