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| Paper IPM / Physic / 6525 |
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| Abstract: | |
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A thorough analysis of the general features of (p=2)-parasupersymmetric
quantum mechanics is presented. It is shown that for both the
Rubakov-Spiridonov (RS) formulation and the Beckers-Debergh (BD) formulation of
(p=2)-parasupersymmetric quantum mechanics, the degeneracy structure of the
energy spectrum can be derived using the defining parasuperalgebras. Thus the
results of this article are independent of the details of the Hamiltonian. In
fact, they are valid for arbitrary systems based on arbitary-dimensional
coordinate manifolds. In particular, the RS and BD systems possess
identical degeneracy structures. For a subclass of RS (alternatively, BD)
systems, a new topological invariant is introduced. This is a counterpart of
the Witten index of supersymmetric quantum mechanics.
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