2016/08/01 by M. V. Ioffe, E. V. Kolevatova, D. N. Nishnianidze
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Diagonalizable matrix #Eigenvalues and eigenvectors #Integrable system #Mathematical physics #Mathematics #Metric (unit) #Minkowski space #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Supercharge #Supersymmetry #Symmetric matrix #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1063/1.4960473
published as Journal of Mathematical Physics, 57 (2016) 082102 · 25 p.p
openalex publication_date 2016/08/01 · arxiv created 2016/08/26 · arxiv updated 2016/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives, the intertwined Hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta. In terms of components, the intertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest—constant—ansatzes for the “metric” matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of “metric” matrices, and their properties are discussed.