Parasupersymmetric quantum mechanics of arbitrary order

Abstract

The parasupersymmetric quantum mechanics of one boson and one parafermion of (arbitrary) order p are constructed. The parasupersymmetry algebra is Q₁^pQ₁⁺= Q₁^p-1Q₁⁺Q₁+...+Q₁ Q₁⁺Q₁^p-1+Q₁+Q₁⁺=2pQ₁^p-1H; Q₁^p+1=0 and (H,Q₁)=0 where Q₁ is the parasupercharge and H is the Hamiltonian. It is also shown that such a system always possesses (p-1) other conserved parasupercharges and p bosonic constants. A model of conformal parasupersymmetry of order p is also discussed and it is shown that in this case the algebra has a particularly simple form.