2014/09/19 by Toshiaki Tanaka, Tanaka, Toshiaki
Materials Science · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Magnetism in coordination complexes #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1409.5578
openalex publication_date 2014/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct quasi-solvable quantum mechanical matrix models by employing two different methods, the one is universal enveloping algebra of Lie superalgebra and the other is N-fold supersymmetry. For the former we examine the q(2) and osp(2/2) Lie-superalgebraic quasi-solvable matrix operators in the literature, and then compare them with the corresponding N-fold supersymmetric matrix systems. In the q(2) case, Lie-superalgebraic construction and the intertwining relation lead to the identical result. In the osp(2/2) case, however, some novel features emerge due to the difference in dimension of linear spaces which consist of the two-component invariant subspace. In both cases, the closure of N-fold superalgebra imposes stronger constraint on the admissible form of the systems and the concept of conjugation plays a key role in the formulation.