math-ph

# Title: Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model

Abstract: A shape invariant nonseparable and nondiagonalizable two-dimensional model with quadratic complex interaction, first studied by Cannata, Ioffe, and Nishnianidze, is re-examined with the purpose of exhibiting its hidden algebraic structure. The two operators $A^+$ and $A^-$, coming from the shape invariant supersymmetrical approach, where $A^+$ acts as a raising operator while $A^-$ annihilates all wavefunctions, are completed by introducing a novel pair of operators $B^+$ and $B^-$, where $B^-$ acts as the missing lowering operator. These four operators then serve as building blocks for constructing ${\mathfrak{gl}}(2)$ generators, acting within the set of associated functions belonging to the Jordan block corresponding to a given energy eigenvalue. This analysis is extended to the set of Jordan blocks by constructing two pairs of bosonic operators, finally yielding an ${\mathfrak{sp}}(4)$ algebra, as well as an ${\mathfrak{osp}}(1/4)$ superalgebra. Hence, the hidden algebraic structure of the model is very similar to that known for the two-dimensional real harmonic oscillator.
 Subjects: Mathematical Physics (math-ph) Journal reference: SIGMA 18 (2022), 004, 11 pages DOI: 10.3842/SIGMA.2022.004 Cite as: arXiv:2010.15273 [math-ph] (or arXiv:2010.15273v2 [math-ph] for this version)

## Submission history

From: Ian Marquette [view email]
[v1] Wed, 28 Oct 2020 23:20:59 GMT (10kb)
[v2] Fri, 14 Jan 2022 06:24:51 GMT (13kb,D)

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