Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-12-01
J.Math.Phys.50:103518,2009
Physics
High Energy Physics
High Energy Physics - Theory
17 pages
Scientific paper
10.1063/1.3231789
We investigate the quantum integrability of the Landau-Lifshitz 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, 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.
Melikyan Armen
Pinzul Aleksandr
No associations
LandOfFree
On quantum integrability of the Landau-Lifshitz model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On quantum integrability of the Landau-Lifshitz model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On quantum integrability of the Landau-Lifshitz model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-718260