Geometric quantization of N=2, D=3 superanyon

TL;DR

This paper develops a quantum model of N=2, D=3 superanyons by combining Berezin and canonical quantization, introducing necessary quantum corrections to preserve supersymmetry.

Contribution

It presents the first quantization of N=2 superanyons with a novel combination of Berezin and canonical methods, including quantum corrections for supersymmetry.

Findings

Renormalized supersymmetry generators are derived.

A consistent first-quantized superanyon model is constructed.

Quantum corrections are essential for supersymmetry preservation.

Abstract

A classical model of N=2, D=3 fractional spin superparticle (superanyon) is presented, whose first-quantization procedure combines the Berezin quantization for the superspin degrees of freedom and the canonical quantization for the space-time ones. To provide the supersymmetry for the quantised theory, certain quantum corrections are required to the N=2 supersymmetry generators as compared to the Berezin procedure. The renormalized generators are found and the first quantised theory of N=2 superanyon is constructed.