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Paper   IPM / Physic / 6525
School of Physics
  Title:   Spectrum Degeneracy of General (P=2)-Parasupersymmetric Quantum Mechanics Parasupersymmetric Topological Invariants
  Author(s):  A. Mostafazadeh
  Status:   Published
  Journal: Int. J. Mod. Phys. A
  No.:  18
  Vol.:  11
  Year:  1996
  Pages:   1057-1076
  Supported by:  IPM
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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