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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References

1. Binegar B., Relativistic field theories in three dimensions, J. Math. Phys. 23 (1982), 1511-1517.
2. Deser S., Jackiw R., Statistics without spin: massless D=3 systems, Phys. Lett. B 263 (1991), 431-436.
3. Sorokin D.P., Volkov D.V., (Anti)commuting spinors and supersymmetric dynamics of semions, Nuclear Phys. B 409 (1993), 547-564.
4. Gorbunov I.V., Kuzenko S.M., Lyakhovich S.L., N=1, D=3 superanyons, OSp(2|2) and the deformed Heisenberg algebra, Phys. Rev. D 56 (1997), 3744-3755, hep-th/9702017.
5. Horvathy P.A., Plyushchay M.S., Valenzuela M., Bosons, fermions and anyons in the plane, and supersymmetry, Ann. Physics 325 (2010), 1931-1975, arXiv:1001.0274.
6. Volkov D.V., Quartions in relativistic field theory, JETP Lett. 49 (1989), 541-543.
7. Sorokin D., The Heisenberg algebra and spin, 3.0.CO;2-J">Fortsch. Phys. 50 (2002), 724-728.
8. Witten E., Supersymmetric index of three-dimensional gauge theory, in The Many Faces of the Superworld, Editor M. Shifman, World Sci. Publ., River Edge, NJ, 2000, 156-184, hep-th/9903005.
9. Pedder C., Sonner J., Tong D., The berry phase of D0-branes, J. High Energy Phys. 2008 (2008), no. 3, 065, 14 pages, arXiv:0801.1813.
10. Mezincescu L., Townsend P.K., Anyons from strings, Phys. Rev. Lett. 105 (2010), 191601, 4 pages, arXiv:1008.2334.
11. Casalbuoni R., The classical mechanics for Bose-Fermi systems, Nuovo Cimento A 33 (1976), 389-431.
12. Brink L., Schwarz J.H., Quantum superspace, Phys. Lett. B 100 (1981), 310-312.
13. Martin J.L., Generalized classical dynamics and the 'classical analogue' of a Fermi oscillator, Proc. Roy. Soc. London. Ser. A 251 (1959), 536-542.
    Martin J.L., The Feynman principle for a Fermi system, Proc. Roy. Soc. London. Ser. A 251 (1959), 543-549.
14. Schonfeld J.F., A mass term for three-dimensional gauge fields, Nuclear Phys. B 185 (1981), 157-171.
15. Cortés J.L., Plyushchay M.S., Anyons as spinning particles, Internat. J. Modern Phys. A 11 (1996), 3331-3362, hep-th/9505117.
16. Siegel W., Hidden local supersymmetry in the supersymmetric particle action, Phys. Lett. B 128 (1983), 397-399.
17. Mezincescu L., Townsend P.K., Semionic supersymmetric solitons, J. Phys. A: Math. Theor. 43 (2010), 465401, 12 pages, arXiv:1008.2775.
18. Townsend P.K., The story of M, in The Future of Theoretical Physics and Cosmology (Cambridge, 2002), Editors G.W. Gibbons, E.P.S. Shellard and S.J. Rankin, Cambridge University Press, Cambridge, 2003, 484-493, hep-th/0205309.
19. Bergshoeff E.A., Hohm O., Rosseel J., Townsend P.K., On maximal massive 3D supergravity, Classical Quantum Gravity 27 (2010), 235012, 24 pages, arXiv:1007.4075.
20. Plyushchay M.S., Operator quantization of massless superparticle, Internat. J. Modern Phys. A 6 (1991), 2497-2517.
21. Klishevich S.M., Plyushchay M.S., Rausch de Traubenberg M., Fractional helicity, Lorentz symmetry breaking and anyons, Nuclear Phys. B 616 (2001), 419-436, hep-th/0101190.