The Quantum 3D Superparticle

TL;DR

This paper quantizes the minimal 3D superparticle, revealing a supermultiplet with fractional spin for non-zero mass and a boson-fermion pair at zero mass, highlighting novel quantum properties in 3D supersymmetry.

Contribution

It provides the first quantization of the minimal 3D superparticle, characterizing its supermultiplet structure with fractional spins and effects of parity-violating terms.

Findings

For non-zero mass, describes a spin-1/4 semion supermultiplet.

Parity-violating term shifts supermultiplet spins by parameter β.

Zero mass case yields a boson-fermion supermultiplet.

Abstract

The minimal (${\cal N}=1$) superparticle in three spacetime dimensions (3D) is quantized. For non-zero mass it describes a spin-1/4 semion supermultiplet of "relativistic helicities" (-1/4, 1/4). The addition of a parity-violating Lorentz-Wess-Zumino term shifts this to $(\beta-1/4,\beta+1/4)$ for arbitrary $\beta$. For zero mass, in which case spin is not defined, the quantum superparticle describes a supermultiplet of one boson and one fermion.