Orthosupersymmetric quantum mechanics

Abstract

We construct a new form of supersymmetric quantum mechanics named orthosupersymmetric quantum mechanics. We show that there are p orthosupercharges Q_α (α= 1,2, …, p) which satisfy the algebra Q_αQ_β^φ+δ_αβ Σ̅φ_γ=1 Q_γ^φQ_γ= 2δ_αβ H,[H,Q_α]= 0 = [H,Q_α^φ]= Q_αQ_β=Q Q_α^φQ_β^φwhere H is the Hamiltonian. The spectra of this class of systems are shown to be (p+1)-fold degenerate, at least above the ground state. We also discuss a model of conformal orthosupersymmetry of degree p and show that in this case there are p orthosupercharges, and p conformal orthosupercharges which along with H, dilatation generator D and conformal generator K form a closed algebra. A comparative discussion on parasupersymmetric and orthosupersymmetric quantum mechanics is also given.