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

Abstract

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 $T^\ast({R}^{1,2})\times{L}^{1|2}$, where the inner K\"ahler supermanifold ${L}^{1|2}=OSp(2|2)/[U(1)\times U(1)]=SU(1,1|2)/[U(2|2)\times U(1)]$ provides the particle with superspin degrees of freedom. We find the relationship between Hamiltonian generators of the global Poincar\'e supersymmetry and the ``internal'' SU(1,1|2) one. Quantization of the superparticle combines the Berezin quantization on ${L}^{1|2}$ 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 ${L}^{1|2}$ underlying their origin is verified. The model admits a smooth contraction to the N=1 supersymmetry in the BPS limit.