We discuss in detail the parasupersymmetric quantum mechanics of arbitrary order where the parasupersymmetry is between the normal bosons and those corresponding to the truncated harmonic oscillator. We show that even though the parasusy algebra is different from that of the usual parasusy quantum mechanics, still the consequences of the two are identical. We further show that the parasupersymmetric quantum mechanics of arbitrary orderp can also be rewritten in terms ofp supercharges (i.e. all of which obeyQi2=0). However, the Hamiltonian cannot be expressed in a simple form in terms of thep supercharges except in a special case. A model of conformal parasupersymmetry is also discussed and it is shown that in this case, thep supercharges, thep conformal supercharges along with HamiltonianH, conformal generatorK and dilatation generatorD form a closed algebra.
Volume 94, 2020
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