Generalized Landau-Lifshitz models on the interval

Details Generalized Landau-Lifshitz models on the interval Generalized Landau-Lifshitz models on the interval

2011-05-25

arxiv.org/abs/1105.5042v2

Nucl.Phys.B853:436-460,2011

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, Latex. Discussion on the continuum limit, and the boundary symmetries added

Scientific paper

10.1016/j.nuclphysb.2011.08.001

We study the classical generalized gl(n) Landau-Lifshitz (L-L) model with special boundary conditions that preserve integrability. We explicitly derive the first non-trivial local integral of motion, which corresponds to the boundary Hamiltonian for the sl(2) L-L model. Novel expressions of the modified Lax pairs associated to the integrals of motion are also extracted. The relevant equations of motion with the corresponding boundary conditions are determined. Dynamical integrable boundary conditions are also examined within this spirit. Then the generalized isotropic and anisotropic gl(n) Landau-Lifshitz models are considered, and novel expressions of the boundary Hamiltonians and the relevant equations of motion and boundary conditions are derived.

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