多粒子SUSY量子力学与置换群表示
Multiparticle SUSY quantum mechanics and the representations of permutation group
摘要：
本文将多维超对称量子力学方法应用于质心运动可分的超对称N粒子系统的研究。新的分解的超哈密顿块对角形式与初等矩阵分量的构造。证明了这些最小块的系数矩阵与置换群SN的不可约表示矩阵一致，对应于Young表（N-M，1^M）。与已知的N粒子Calogero和Sutherland模型的推广的连接建立。
英文摘要：
The method of multidimensional SUSY Quantum Mechanics is applied to the investigation of supersymmetrical N-particle systems on a line for the case of separable center-of-mass motion. New decompositions of the superhamiltonian into block-diagonal form with elementary matrix components are constructed. Matrices of coefficients of these minimal blocks are shown to coincide with matrices of irreducible representations of permutations group S_N, which correspond to the Young tableaux (N-M,1^M). The connections with known generalizations of N-particle Calogero and Sutherland models are established.
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