We consider the problem of bosonizing supersymmetric quantum mechanics (SSQM) and some of its variants, i.e., of realizing them in terms of only boson-like operators without fermion-like ones. In the SSQM case, this is realized in terms of the generators of the Calogero-Vasiliev algebra (also termed deformed Heisenberg algebra with reflection). In that of the SSQM variants, this is done by considering generalizations of the latter algebra, namely the $C_{ \lambda}$-extended oscillator algebras, where $C_{ \lambda}$ is the cyclic group of order~$\lambda$.
Categories: math-ph hep-th math.MP quant-ph