交换超算符方法的李代数研究

本文讨论了交换超算符方法的理论基础,结果表明由交换超算符所定义的算符集合g是一个李代数,交换超算符的定义就是李代数中内导子的定义,由此得出一些交换超算符间的代数关系。证明了g中所有算符诱导的超算符集合也是一个李代数,指出了与g对应的是由复盖群派生的,有内积定义的李群,而角动量超算符是由矢量场的内禀角动量和单位算符的直积所生成。结论是交换超算符方法的理论基础是李代数。

LIE ALGEBRIC RESEACH OF COMMUTATIVE HYPER-OPERATOR METHOD

In this paper the theoretical foundation of commutative hyper-operator method has been discussed.The results show that the operator set defined by commutative hyperoper-ator is a Lie algebra, the definition of commutative hyper-operator is just that of the inner derivation in Lie algebra.From this, some algebric relations between commutative hyper-operators were obtained. It is verified that hyper-opera tor set derived from operators in g is also a Lie algebra.It is shown that a Lie group derived from covering group and defined by inner product corresponds to g.and the hyper-operators of angular momentum are generated by direct product between inner angular momentum of a vector field and unit operator.The conclusion is that the theoretical foundation of commutative hyper-operator method is Lie algebra.