Minimal bosonization of double-graded quantum mechanics

The superalgebra of ℤ22-graded supersymmetric quantum mechanics is shown to be realizable in terms of a single bosonic degree of freedom. Such an approach is directly inspired by a description of the corresponding ℤ2-graded superalgebra in the framework of a Calogero–Vasiliev algebra or, more generally, of a generalized deformed oscillator algebra. In the case of the ℤ22-graded superalgebra, the central element Z has the property of distinguishing between degenerate eigenstates of the Hamiltonian.

Note:

11 pages, no figure, published version

Supersymmetric quantum mechanics
ℤ22-graded superalgebras
deformed oscillator algebras
03.65.Fd
11.30.Pb
quantum mechanics: supersymmetry
algebra: graded
supersymmetry: algebra
Z(2)
oscillator: deformation

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