Continual classical Heisenberg models defined on graded su(2,1) and su(3) algebras

Continual integrable Heisenberg models are constructed on real subalgebras of the superalgebra spl(2/1). Two Heisenberg models are shown to exist on the compact subalgebra uspl(2/1)≊su(2/1). One of these, SU(2/1)/S(U(2)×U(1)), is gauge equivalent to SU(2) nonlinear vector Schrodinger equation (NLSE) expressed in odd Grassman variables, the other, SU(2/1)/S(L(1/1)×U(1)), to ‘‘super’’ NLSE which is invariant under global supersymmetry transformations of SL(1/1). Also constructed are a Heisenberg model on the noncompact subalgebra ospu(1,1/1), with higher nonlinearities, and its gauge equivalent analog. Hamiltonian structure and classical solutions are studied and the possible connection of the given models with a version of the Hubbard one is discussed.

[1]  V. Makhankov,et al.  Supersymmetric integrable su(2…1) Heisenberg models , 1989 .

[2]  Y. .. Zhou.  Integrable quantum reductions of a manycomponent magnetic system (a comment) , 1989 .

[3]  V. G. Makhankov,et al.  Gauge equivalence, supersymmetry and classical solutions of the ospu (1, 1/1) Heisenberg model and the nonlinear Schrödinger equation , 1988, 1612.09124.

[4]  Wiegmann,et al.  Superconductivity in strongly correlated electronic systems and confinement versus deconfinement phenomenon. , 1988, Physical review letters.

[5]  V. Man'ko,et al.  Group Theoretical Methods in Physics , 1987 .

[6]  P. Anderson.  The Resonating Valence Bond State in La2CuO4 and Superconductivity , 1987, Science.

[7]  A. Perelomov.  Generalized Coherent States and Their Applications , 1986 .

[8]  O. Pashaev,et al.  Nonlinear σ-models with noncompact symmetry group in the theory of a nearly ideal bose gas , 1986 .

[9]  P. P. Kulish.  Quantum OSP-invariant nonlinear Schrödinger equation , 1985 .

[10]  A. Quattropani,et al.  Two-photon absorption in atoms and solids , 1983 .

[11]  V. Makhankov,et al.  On the gauge equivalence of the Landau-Lifshitz and the nonlinear Schrödinger equations on symmetric spaces , 1983 .

[12]  V. Korepin,et al.  Lattice versions of quantum field theory models in two dimensions , 1982 .

[13]  V. Makhankov,et al.  A new integrable model of quantum field theory in the state space with indefinite metric , 1982 .

[14]  Edward Witten,et al.  Dynamical Breaking of Supersymmetry , 1981 .

[15]  T. Regge,et al.  Geometrical formulation of supergravity theories on orthosymplectic supergroup manifolds , 1980 .

[16]  G. Soliani,et al.  Nonlinear Evolution Equations and Dynamical Systems , 1980 .

[17]  C. P. Yang,et al.  Ground-State Energy of a Heisenberg-Ising Lattice , 1966 .

[18]  J. Hubbard.  Electron correlations in narrow energy bands , 1963, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.