On quantum integrability of the Landau-Lifshitz model


Autoria(s): MELIKYAN, A.; PINZUL, A.
Contribuinte(s)

UNIVERSIDADE DE SÃO PAULO

Data(s)

18/04/2012

18/04/2012

2009

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

http://dx.doi.org/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