Superconformal Quantum Mechanics via Wigner-Heisenberg Algebra

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.

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