Superconformal Quantum Mechanics via Wigner-Heisenberg Algebra

TL;DR

This paper explores the connection between Wigner-Heisenberg algebra and superconformal quantum mechanics, introducing a model with conformal symmetry, defining its spectrum and operators, and relating it to known models like Calogero and Dirac Oscillator.

Contribution

It presents a novel superconformal quantum mechanics model based on Wigner-Heisenberg algebra with explicit spectrum and operator definitions, extending previous models.

Findings

The model exhibits superconformal symmetry within the Wigner-Heisenberg framework.

The energy spectrum and Casimir operator are explicitly constructed.

The Hamiltonian relates to Calogero and Dirac Oscillator models.

Abstract

We show the natural relation between the Wigner Hamiltonian and the conformal Hamiltonian. It is presented a model in (super)conformal quantum mechanics with (super)conformal symmetry in the Wigner-Heisenberg algebra picture $ [x,p_{x}]= i(1+c{\bf P})$ (${\bf P}$ being the parity operator). In this context, the energy spectrum, the Casimir operator, creation and annihilation operators are defined. This superconformal Hamiltonian is similar to the super-Hamiltonian of the Calogero model and it is also an extension of the super-Hamiltonian for the Dirac Oscillator.