Parasupersymmetry and N-fold Supersymmetry in Quantum Many-Body Systems II. Third Order

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dc.creatorTanaka, Toshiaki
dc.date2006-12-25
dc.date2007-03-09
dc.date.accessioned2026-07-07T11:23:30Z
dc.date.available2026-07-07T11:23:30Z
dc.descriptionBased on the general formalism of parafermionic algebra and parasupersymmetry proposed previously by us, we explicitly construct third-order parafermionic algebra and multiplication law, and then realize third-order parasupersymmetric quantum systems. We find some novel features in the third-order, namely, the emergence of a fermionic degree of freedom and of a generalized parastatistics. We show that for one-body cases the generalized Rubakov-Spiridonov model can be constructed also in our framework and find that it admits a generalized 3-fold superalgebra. We also find that a three-body system can have third-order parasupersymmetry where three independent supersymmetries are folded. In both cases, we also investigate the new concept of quasi-parasupersymmetry introduced by us and find that those of order (3,3) are indeed realized under less restrictive conditions than (ordinary) parasupersymmetric cases.
dc.description22 pages, no figures; minor typos corrected, version to appear in Annals of Physics
dc.identifierhttps://arxiv.org/abs/hep-th/0612263
dc.identifierhttp://arxiv.org/abs/hep-th/0612263
dc.identifierAnnalsPhys.322:2682-2702,2007
dc.identifierdoi:10.1016/j.aop.2007.01.004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/194911
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.titleParasupersymmetry and N-fold Supersymmetry in Quantum Many-Body Systems II. Third Order
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