Fuzzy CP(n|m) as a quantum superspace
High Energy Physics - Theory
2007-05-23 v3
Abstract
The `Chern-Simons Quantum Mechanics' of a particle on CP(n|m) is shown to yield the fuzzy descriptions of these superspaces, for which we construct the non-(anti)commuting position operators. For a particle on the supersphere CP(1|1) = SU(2|1)/U(1|1), the particle's wave-function at fuzziness level 2s is shown to be a degenerate irrep of SU(2|1) describing a supermultiplet of SU(2) spins (s-1\2, s).
Cite
@article{arxiv.hep-th/0311159,
title = {Fuzzy CP(n|m) as a quantum superspace},
author = {Evgeny Ivanov and Luca Mezincescu and Paul K. Townsend},
journal= {arXiv preprint arXiv:hep-th/0311159},
year = {2007}
}
Comments
19 pp. Contribution to "Symmetries in Gravity and Field Theory", conference for Jose-Adolfo de Azcarraga's 60th birthday, June 2003, Salamanca, Spain. Minor corrections made and references included. Notation clarified, and additional reference in v.3