2003/01/31 by A. A. Andrianov, А. В. Соколов, A. V. Sokolov · 4 citations
Mathematics · Physics and Astronomy · #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1016/s0550-3213(03)00232-3
published as Nucl.Phys. B660 (2003) 25-50 · 28 pages, Latex, minor improvements and removed misprints
arxiv created 2003/03/18 · openalex publication_date 2003/05/19 · arxiv updated 2010/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We study the Nonlinear (Polynomial, N-fold,...) Supersymmetry algebra in one-dimensional QM. Its structure is determined by the type of conjugation operation (Hermitian conjugation or transposition) and described with the help of the Super-Hamiltonian projection on the zero-mode subspace of a supercharge. We show that the SUSY algebra with transposition symmetry is always polynomial in the Hamiltonian if supercharges represent differential operators of finite order. The appearance of the extended SUSY with several (complex or real) supercharges is analyzed in details and it is established that no more than two independent supercharges may generate a Nonlinear superalgebra which can be appropriately specified as \cal N = 2 SUSY. In this case we find a non-trivial hidden symmetry operator and rephrase it as a non-linear function of the Super-Hamiltonian on the physical state space. The full \cal N = 2 Non-linear SUSY algebra includes "central charges" both polynomial and non-polynomial (due to a symmetry operator) in the Super-Hamiltonian.