Extended Fractional Supersymmetric Quantum Mechanics

TL;DR

This paper introduces a new realization of fractional supersymmetric quantum mechanics using tensor products of paragrassmann variables, revealing q-deformed relations between conserved charges, expanding the algebraic structure of the theory.

Contribution

It presents an alternative algebraic realization of fractional supersymmetry with tensor products of paragrassmann variables and q-deformed relations, advancing the mathematical framework.

Findings

New algebraic realization using tensor products of paragrassmann variables.

Discovery of q-deformed relations between conserved charges.

Extension of fractional supersymmetric quantum mechanics algebra.

Abstract

Recently, we presented a new class of quantum-mechanical Hamiltonians which can be written as the $F^{th}$ power of a conserved charge: $H=Q^F$ with $F=2,3,...\,.$ This construction, called fractional supersymmetric quantum mechanics, was realized in terms of a paragrassmann variable $\theta$ of order $F$, which satisfies $\theta^F=0$. Here, we present an alternative realization of such an algebra in which the internal space of the Hamiltonians is described by a tensor product of two paragrassmann variables of orders $F$ and $F-1$ respectively. In particular, we find $q$-deformed relations (where $q$ are roots of unity) between different conserved charges. (To appear in "Mod.Phys.Lett.A")