Chiral super-Tremblay-Turbiner-Winternitz Hamiltonians and their dynamical superalgebra

TL;DR

This paper introduces a new chiral supersymmetric extension of the Tremblay-Turbiner-Winternitz Hamiltonians, revealing a dynamical superalgebra with atypical lowest-weight representations, expanding the understanding of their symmetry structure.

Contribution

It presents a novel chiral supersymmetric extension of TTW Hamiltonians and analyzes their associated superalgebra with atypical representations, differing from previous models.

Findings

New chiral supersymmetric TTW Hamiltonians constructed

Superalgebra exhibits atypical lowest-weight representations

Extension parallels magnetic monopole supersymmetry studies

Abstract

The family of Tremblay-Turbiner-Winternitz (TTW) Hamiltonians $H_k$ on a plane, corresponding to any positive real value of $k$, is shown to admit another ${\cal N} = 2$ supersymmetric extension than that previously introduced by the present author. This new extension is of the same kind as that considered by D'Hoker and Vinet in the study of magnetic monopoles and is characterized by the fact that all the irreducible representations of the corresponding ${\rm osp}(2/2, \R)$ dynamical superalgebra are atypical lowest-weight state ones. The new supersymmetric Hamiltonians may be referred to as chiral super-TTW Hamiltonians, the role of chirality being played here by the fermion number parity operator.