Quantum integrable systems, non-skew-symmetric r-matrices and algebraic Bethe ansatz

Journal Article · Thu Feb 15 00:00:00 EST 2007 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2435085· OSTI ID:20929643

Skrypnyk, T ^[1]

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1. Bogoliubov Institute for Theoretical Physics, Institute of Mathematics of NASU, Metrologichna Strasse, 14-b, Kiev 03143 (Ukraine)

We prove the integrability of the general quantum Hamiltonian systems governed by an arbitrary non-skew-symmetric, so(3)-valued, nondynamical classical r-matrix with spectral parameters. We consider the most interesting example of these quantum integrable systems, namely, the so(3) 'generalized Gaudin systems' in detail. In the case of an arbitrary r-matrix which is 'diagonal' in the sl(2) basis we calculate the spectrum and the eigenvalues of the corresponding Hamiltonians using the algebraic Bethe ansatz technique.

• OSTI ID: 20929643
• Journal Information: Journal of Mathematical Physics, Vol. 48, Issue 2; Other Information: DOI: 10.1063/1.2435085; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
EIGENFUNCTIONS
EIGENVALUES
HAMILTONIANS
INTEGRAL CALCULUS
LATTICE FIELD THEORY
R MATRIX
SO-3 GROUPS