Lie-Poisson框架下的Dirac-Bargmann系统的可积性

Integrability of Dirac-Bargmann system in the Lie-Poisson framework

研究和Lie代数so(2,1)对应的3×3 Dirac谱问题的非线性化,证明了该系统的非线性化特征值问题是具有Lie-Poisson结构的Poisson流形R3N上的广义Hamilton系统.进一步利用母函数法给出其可积性的证明.

The nonlinearization of a3×3Dirac spectral problem associated with Lie algebra so(2,1)is presented.It is shown that this nonlinearized eigenvalue problem is a generalized Hamiltonian system with Lie-Poisson structure on the Poisson manifold R 3N.Further,its integrability is given by the generating function method.