Two-Dimensional Supersymmetry: From SUSY Quantum Mechanics to Integrable Classical Models

Abstract

Two known 2-dim SUSY quantum mechanical constructions - the direct generalization of SUSY with first-order supercharges and Higher order SUSY with second order supercharges - are combined for a class of 2-dim quantum models, which {\it are not amenable} to separation of variables. The appropriate classical limit of quantum systems allows us to construct SUSY-extensions of original classical scalar Hamiltonians. Special emphasis is placed on the symmetry properties of the models thus obtained - the explicit expressions of quantum symmetry operators and of classical integrals of motion are given for all (scalar and matrix) components of SUSY-extensions. Using Grassmanian variables, the symmetry operators and classical integrals of motion are written in a unique form for the whole Superhamiltonian. The links of the approach to the classical Hamilton-Jacobi method for related "flipped" potentials are established.

19 pages

References in corpus (27)

• Supersymmetry and Quantum Mechanics
• Higher-Derivative Supersymmetry and the Witten Index
• Second Order Derivative Supersymmetry and Scattering Problem
• Polynomial SUSY in Quantum Mechanics and Second Derivative Darboux Transformation
• Nonlinear supersymmetry in Quantum Mechanics: algebraic properties and differential representation
• Nonlinear Supersymmetry for Spectral Design in Quantum Mechanics
• General Forms of a N-fold Supersymmetric Family
• Nonlinear Supersymmetry, Quantum Anomaly and Quasi-Exactly Solvable Systems
• New possibilities for supersymmetry breakdown in quantum mechanics and second order irreducible Darboux transformations
• New Methods for Two-Dimensional Schrödinger Equation: SUSY-separation of Variables and Shape Invariance
• Matrix Hamiltonians: SUSY approach to hidden symmetries
• SUSY-Approach for Investigation of Two-Dimensional Quantum Mechanical Systems
• Quantum Inozemtsev model, quasi-exact solvability and N-fold supersymmetry
• Two-dimensional SUSY-pseudo-Hermiticity without separation of variables
• Algebraic Solution of the Supersymmetric Hydrogen Atom in d Dimensions
• Chains of Darboux transformations for the matrix Schroedinger equation
• SUSY Intertwining Relations of Third Order in Derivatives
• Extended Supersymmetries and the Dirac Operator
• New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach
• Classical Integrable 2-dim Models Inspired by SUSY Quantum Mechanics
• Pauli equation and the method of supersymmetric factorization
• sl(2) Construction of Type A N-fold supersymmetry
• Multiparticle SUSY quantum mechanics and the representations of permutation group
• Intertwining Relations for the Matrix Calogero-like Models: Supersymmetry and Shape Invariance
• On two-dimensional superpotentials: from classical Hamilton-Jacobi theory to 2D supersymmetric quantum mechanics
• Supersymmetry versus Integrability in two-dimensional Classical Mechanics
• The classical supersymmetric Coulomb problem

Cited by in corpus (12)

• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• Exact Solvability of Two-Dimensional Real Singular Morse Potential
• A Class of Partially Solvable Two-Dimensional Quantum Models with Periodic Potentials
• Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics
• New Exactly Solvable Two-Dimensional Quantum Model Not Amenable to Separation of Variables
• New Two-Dimensional Quantum Models with Shape Invariance
• Pseudospin symmetry in nuclear structure and its supersymmetric representation
• Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force
• Degeneracy and coherent states of the two-dimensional Morse potential
• On two-dimensional supersymmetric quantum mechanics, pseudoanalytic functions and transmutation operators
• Coherent states of the two-dimensional non-separable supersymmetric Morse potential
• Singular parametric oscillators from the one-parameter Darboux transformation of the classical harmonic oscillator