The Quantum 3D Superparticle

The minimal ($\mathcal{N}=1$) 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 $(\beta -1\mathrm{/}4,\beta +1\mathrm{/}4)$ 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.