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

M. V. Ioffe·J. Mateos Guilarte·P. A. Valinevich
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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.

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BibTeXRIS

M. V. Ioffe, J. Mateos Guilarte, P. A. Valinevich. 2006-03-01. Two-Dimensional Supersymmetry: From SUSY Quantum Mechanics to Integrable Classical Models. https://doi.org/10.1016/j.aop.2006.02.011

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