Hidden supersymmetry and Berezin quantization of $N=2,$ $D=3$ spinning superparticles

The first quantized theory of $N=2,$ $D=3$ massive superparticles with arbitrary fixed central charge and (half) integer or fractional superspin is constructed. The quantum states are realized on the fields carrying a finite-dimensional, or a unitary infinite-dimensional, representation of the supergroups OSp (2|2) or SU (1,1|2). The construction originates from quantization of a classical model of the superparticle we suggest. The physical phase space of the classical superparticle is embedded in a symplectic superspace $T*(R1,2)×L1|2,$ where the inner Kähler supermanifold $L1|2≅OSp(2|2)/[U(1)×U(1)]≅SU(1,1|2)/[U(2|2)×U(1)]$ provides the particle with superspin degrees of freedom. We find the relationship between Hamiltonian generators of the global Poincaré supersymmetry and the “internal” SU(1,1|2) one. Quantization of the superparticle combines the Berezin quantization on $L1|2$ and the conventional Dirac quantization with respect to space–time degrees of freedom. Surprisingly, to retain the supersymmetry, quantum corrections are required for the classical $N=2$ supercharges as compared to the conventional Berezin method. These corrections are derived and the Berezin correspondence principle for $L1|2$ underlying their origin is verified.