Continual classical Heisenberg models defined on graded su(2,1) and su(3) algebras
Continual classical Heisenberg models defined on graded su(2,1) and su(3) algebras
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DOI：
10.1063/1.529561
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发表时间：
1992-08
影响因子：
1.3
通讯作者：
V. Makhankov;O. Pashaev
中科院分区：
文献类型：
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作者：
V. Makhankov;O. Pashaev
连续可积海森堡模型是在超代数 spl(2/1) 的实子代数上构建的。两个海森堡模型被证明存在于紧子代数 uspl(2/1)≊su(2/1) 上。其中一个，SU(2/1)/S(U(2)×U(1))，规范等价于以奇格拉斯曼变量表示的 SU(2) 非线性向量薛定谔方程 (NLSE)，另一个，SU(2/1)/S(L(1/1)×U(1))，相当于“超级”NLSE，其在 SL(1/1) 的全局超对称变换下保持不变。还构建了非紧子代数 ospu(1,1/1) 上的海森堡模型（具有更高的非线性）及其规范等效模拟。研究了哈密顿结构和经典解，并讨论了给定模型与哈伯德模型的一种版本的可能联系。
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.