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 $(\beta -1/4,\beta+1/4)$ 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.