Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-03-25
Int.J.Mod.Phys.A12:2725-2740,1997
Physics
High Energy Physics
High Energy Physics - Theory
Some explanations added. LaTeX file, 17 pages
Scientific paper
10.1142/S0217751X9700150X
The general features of the degeneracy structure of ($p=2$) parasupersymmetric quantum mechanics are employed to yield a classification scheme for the form of the parasupersymmetric Hamiltonians. The method is applied to parasupersymmetric systems whose Hamiltonian is the square root of a forth order polynomial in the generators of the parasupersymmetry. These systems are interesting to study for they lead to the introduction of a set of topological invariants very similar to the Witten indices of ordinary supersymmetric quantum mechanics. The topological invariants associated with parasupersymmetry are shown to be related to a pair of Fredholm operators satisfying two compatibility conditions. An explicit algebraic expression for the topological invariants of a class of parasupersymmetric systems is provided.
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