Superconformal Quantum Mechanics via Wigner-Heisenberg Algebra

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 $[x,p_x]=i(1+c\mathbf{P})$ ($\mathbf{P}$ 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.

14 pages, 2 figures. Revised version with corrections and additional arguments

References in corpus (8)

• AdS_2/CFT_1, Canonical Transformations and Superconformal Mechanics
• The non-commutative and discrete spatial structure of a 3D Wigner quantum oscillator
• Comments on N=4 Superconformal Extension of the Calogero Model
• A non-commutative n-particle 3D Wigner quantum oscillator
• Generalized Calogero model in arbitrary dimensions
• On the Hydrogen Atom via Wigner-Heisenberg Algebra
• Representations of the Lie Superalgebra gl(1|n) in a Gel'fand-Zetlin Basis and Wigner Quantum Oscillators
• Dirac Oscillator via R-Deformed Heisenberg Algebra

Cited by in corpus (1)

• Non-Hermitian Oscillator and R-deformed Heisenberg Algebra