On quantum integrability of the Landau-Lifshitz model

Autor(es)

Melikyan, A. ^[1] ; Pinzul, A. ^[2]

Afiliação do(s) autor(es)

^[1] Int Ctr Condensed Matter Phys, BR-70919970 Brasilia, DF - Brazil

^[2] Univ Sao Paulo, Inst Fis, BR-05315970 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Physics; v. 50, n. 10 OCT 2009.
• Citações Web of Science: 10

Resumo

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)

• Processo FAPESP: 05/05147-3 - Integrabilidade da teoria de cordas
• Beneficiário: Arsen Melikyan
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 06/56056-0 - Methods and applications of noncommutative geometry: twisted symmetry and quantum gravity
• Beneficiário: Aleksandr Nikolaievich Pinzul
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado