Positive discrete series of osp(\(2{|}2,{\mathbb{R}})\) and (para)supersymmetric quantum mechanics. (English) Zbl 0779.17028
Just as bosonic or fermionic operators are defined by means of a bilinear relation, parabosonic and parafermionic operators are defined through a trilinear relation. Their Fock spaces are characterized by one number, the order of paraquantization. Here, it is shown that the superposition of one paraboson and one parafermion of the same order gives rise to a realization of the Lie superalgebra \(\text{osp}(2/2,\mathbb{R})\), and the Fock spaces correspond to irreducible positive discrete series representations of \(\text{osp}(2/2,\mathbb{R})\), which can be typical or atypical. The parasupersymmetric spectra are then analyzed in these representations.
Reviewer: J.Van der Jeugt (Gent)
MSC:
| 17B81 | Applications of Lie (super)algebras to physics, etc. |
| 81Q60 | Supersymmetry and quantum mechanics |
| 17B70 | Graded Lie (super)algebras |
Keywords:
parabosons; orthosymplectic superalgebras; Lie superalgebra \(\text{osp}(2/2,R)\); Fock spaces; discrete series representations; parasupersymmetric spectraReferences:
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