Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 005, 11 pages      arXiv:1011.5049      https://doi.org/10.3842/SIGMA.2011.005
Contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design”

The Quantum 3D Superparticle

Luca Mezincescu a and Paul K. Townsend b
a) Department of Physics, University of Miami, Coral Gables, FL 33124, USA
b) Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK

Received November 29, 2010, in final form January 05, 2011; Published online January 10, 2011

Abstract
The minimal (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 (β−1/4,β+1/4) for arbitrary β. For zero mass, in which case spin is not defined, the quantum superparticle describes a supermultiplet of one boson and one fermion.

Key words: superparticle; semion.

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