Parasupersymmetric Quantum Mechanics and Indices of Fredholm Operators

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.

arXiv commentSome explanations added. LaTeX file, 17 pages

Cited by in corpus (8)

• Quantum Mechanical Symmetries and Topological Invariants
• Topological Symmetries
• Supersymmetric Many-Body Systems from Partial Symmetries: Integrability, Localization and Scrambling
• On the generalized unitary parasupersymmetry algebra of Beckers-Debergh
• On the Statistical Origin of Topological Symmetries
• Parasupersymmetry and N-fold Supersymmetry in Quantum Many-Body Systems I. General Formalism and Second Order
• On a Z_3-Graded Generalization of the Witten Index
• Parasupersymmetry and N-fold Supersymmetry in Quantum Many-Body Systems II. Third Order