On quantum integrability of the Landau-Lifshitz model
Contribuinte(s) |
UNIVERSIDADE DE SÃO PAULO |
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Data(s) |
18/04/2012
18/04/2012
2009
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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. FAPESP[05/05147-3] FAPESP[06/56056-0] Brazilian Ministry of Science and Technology - MCT Ministério de Ciência e Tecnologia Instituto Brasileiro de Energia e Materiais (IBEM) |
Identificador |
JOURNAL OF MATHEMATICAL PHYSICS, v.50, n.10, 2009 0022-2488 http://producao.usp.br/handle/BDPI/16360 10.1063/1.3231789 |
Idioma(s) |
eng |
Publicador |
AMER INST PHYSICS |
Relação |
Journal of Mathematical Physics |
Direitos |
openAccess Copyright AMER INST PHYSICS |
Palavras-Chave | #integration #mathematical operators #matrix decomposition #quantum theory #S-matrix theory #HEISENBERG SPIN CHAIN #LINEAR SCHRODINGER-EQUATION #INVERSE SCATTERING METHOD #YANG-BAXTER EQUATION #LOCAL HAMILTONIANS #BETHE-ANSATZ #LATTICE #SOLITONS #REPRESENTATIONS #QUANTIZATION #Physics, Mathematical |
Tipo |
article original article publishedVersion |