bosonic operators. Such a construction gives us a possibility to realize a Bose-Fermi transformation in terms of one bosonic oscillator and construct a spin-1/2 representation of the SU(2) group on its Fock space. We shall show that the realization of N=2 supersymmetric quantum mechanics on the Fock space of the bosonic oscillator is achieved due to a specific nonlocal character of the supersymmetry generators. Hence, from the point of view of a nonlocality, the bosonization scheme turns out to be similar to the above mentioned Chern-Simons gauge field constructions for anyons [@sem; @sred]. Then, we shall generalize the constructions to the more complicated $N=2$ supersymmetric systems, in particular, corresponding to the Witten supersymmetric quantum mechanics with odd superpotential. In conclusion of this section, we shall demonstrate that the construction can be extended to the case of OSp(2$\vert$2) supersymmetry. As a consequence, we reveal $osp(2\vert 2)$ superalgebra in the form of the operator superalgebra for the quantum mechanical 2-body (nonsupersymmetric) Calogero model [@caloj].

Section 6 is devoted to the discussion of the results, open problems and possible generalizations of the constructions.

Within a group-theoretical approach to anyons, relativistic field with fractional (arbitrary) spin $s$ can be described by the system of 