Para, pseudo, and orthosupersymmetric quantum mechanics and their bosonization

Abstract

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~$\lambda$.