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

摘要

Two known 2-dim SUSY quantum mechanical constructions - the directgeneralization of SUSY with first-order supercharges and Higher order SUSY withsecond order supercharges - are combined for a class of 2-dim quantum models,which {\it are not amenable} to separation of variables. The appropriateclassical limit of quantum systems allows us to construct SUSY-extensions oforiginal classical scalar Hamiltonians. Special emphasis is placed on thesymmetry properties of the models thus obtained - the explicit expressions ofquantum symmetry operators and of classical integrals of motion are given forall (scalar and matrix) components of SUSY-extensions. Using Grassmanianvariables, the symmetry operators and classical integrals of motion are writtenin a unique form for the whole Superhamiltonian. The links of the approach tothe classical Hamilton-Jacobi method for related "flipped" potentials areestablished.