Abstract
Supersymmetric quantum mechanics cannot be deformed when the superposition of only a pair of usual bosons and fermions is considered, but it can if nontrivial parabosons and parafermions of the same order p of paraquantization are superposed. We take the simplest case p=2 and exhibit reducibility problems in that context by using Green–Cusson Ansätze following Macfarlane methods. Specific representations of the Lie superalgebra osp (2|2, R) play an interesting role in connection with possible deformations.
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