Fractional Supersymmetry and Quantum Mechanics

Abstract

We present a set of quantum-mechanical Hamiltonians which can be written as the $F^{\mathrm{th}}$ power of a conserved charge: $H=Q^F$ with $[H,Q]=0$ and $F=2,3,....$ This new construction, which we call {\it fractional}\/ supersymmetric quantum mechanics, is realized in terms of \pg\ variables satisfying $\t^F=0$. Furthermore, in a pseudo-classical context, we describe {\it fractional}\/ supersymmetry transformations as the $F^{\mathrm{th}}$ roots of time translations, and provide an action invariant under such transformations.

12 pages, plain TEX, McGill/92-54, to appear in Phys. Lett. B (minor corrections and references updated)

References in corpus (4)

• Paragrassmann Analysis and Quantum Groups
• Fractional Superspace Formulation of Generalized Super-Virasoro Algebras
• Fractional Supersymmetry
• Extended Fractional Supersymmetric Quantum Mechanics

Cited by in corpus (24)

• Group Theoretical Foundations of Fractional Supersymmetry
• Double-Graded Supersymmetric Quantum Mechanics
• 2D Fractional Supersymmetry for Rational Conformal Field Theory. Application for Third-Integer Spin States
• Fractional supersymmetric Quantum Mechanics as a set of replicas of ordinary supersymmetric Quantum Mechanics
• Quantum Mechanical Symmetries and Topological Invariants
• Fractional supersymmetry and hierarchy of shape invariant potentials
• Minimal bosonization of double-graded supersymmetric quantum mechanics
• A Novel Multi-parameter Family of Quantum Systems with Partially Broken N-fold Supersymmetry
• Extended Fractional Supersymmetric Quantum Mechanics
• Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions
• Coherent state quantization of paragrassmann algebras
• Topological Symmetries
• A note on Gaussian integrals over paragrassmann variables
• On the Representation Theory of Orthofermions and Orthosupersymmetric Realization of Parasupersymmetry and Fractional Supersymmetry
• Non-Abelian Fractional Supersymmetry in Two Dimensions
• Midgap States and Generalized Supersymmetry in Semi-infinite Nanowires
• On the Statistical Origin of Topological Symmetries
• Reducibility and bosonization of parasupersymmetric and orthosupersymmetric quantum mechanics
• On Linear Differential Equations Involving a Para-Grassmann Variable
• On a Z_3-Graded Generalization of the Witten Index
• Two dimensional fractional supersymmetric conformal field theories and the two point functions
• Simultaneous Ordinary and Type A N-fold Supersymmetries in Schroedinger, Pauli, and Dirac Equations
• N-fold Parasupersymmetry
• Fractional Supersymmetry As a Matrix Model