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arXiv · hep-th/9603163

Parasupersymmetric Quantum Mechanics and Indices of Fredholm Operators

Ali Mostafazadeh
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Abstract

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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Ali Mostafazadeh. 1996-07-03. Parasupersymmetric Quantum Mechanics and Indices of Fredholm Operators. https://doi.org/10.1142/s0217751x9700150x

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