Multiparticle SUSY quantum mechanics and the representations of permutation group

Details Multiparticle SUSY quantum mechanics and the representations of permutation group Multiparticle SUSY quantum mechanics and the representations of permutation group

2000-01-18

arxiv.org/abs/quant-ph/0001063v1

J.Phys.A33:1581,2000

Physics

Quantum Physics

20 pages, Latex,no figures

Scientific paper

10.1088/0305-4470/33/8/305

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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