Minimal Realizations of Supersymmetry for Matrix Hamiltonians
Alexander A. Andrianov, Andrey V. Sokolov
TL;DR
This paper introduces criteria for minimal realizations of supersymmetry in matrix Hamiltonians, providing methods to construct Hamiltonians with specified symmetry matrices and analyzing their structural properties.
Contribution
It presents new criteria for weak and strong minimizability of matrix intertwining operators and offers a construction method for matrix Hamiltonians with given symmetry matrices.
Findings
Criteria for strong minimizability of matrix intertwining operators.
Conditions for the existence of constant symmetry matrices.
Method for constructing matrix Hamiltonians with specified symmetries.
Abstract
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant symmetry matrix for a matrix Hamiltonian are presented. A method of constructing of a matrix Hamiltonian with a given constant symmetry matrix in terms of a set of arbitrary scalar functions and eigen- and associated vectors of this matrix is offered. Examples of constructing of matrix Hamiltonians with given symmetry matrices for the cases of different structure of Jordan form of these matrices are elucidated.
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