阶化SU(3)与基本粒子分类

GRADE SU(3)AND CLASSIFICATION OF PARTICLES

本文通过阶化李代数的方法将时空对称的Poincaré代数与内对称的SU(3)代数结合.在对基本代数假定之后,找出了该代数的Casimir算子并加以严格证明.并用若干个相互对易的厄米矩阵同时对角化的方法,对该代数在静止架中小代数最低维表示的超多重态的(J,I,Y)内容进行了计算.

In this paper we discuss a algebra,which combine poincare algebra of spacetimesymmetry with the SU(3)algebra of internal symmetry via Grade Lie algebra.After giving thebasic assumption of the algebra,the Casimirs of the algebra have been found and proved strictly.The(J,I,Y)contents of the lowest super multiplet representation of the little algebra in sta-tionery frame have been calculated using the simultaniously diagonalization of Hermitian matriceswhich are commutative each other.