Bosonized supersymmetric quantum mechanics and supersymmetry of parabosons (parafermions)∗

We review the construction of minimally bosonized supersymmetric quantum mechanics and its relation to hidden supersymmetries in pure parabosonic (parafermionic) systems. The simplest N = 1 supersymmetric quantum mechanical system is the superoscillator [1] given by the Hamiltonian H = 1 2 {b, b−}+ 1 2 [f, f−]. (1) In addition to H , the system is characterized by the two conserved integrals of motion (supercharges) Q± = b ∓f±, (2) which are quadratic in bosonic (b±) and fermionic (f±) creation-annihilation operators. The operator Γ = [f, f−] has a sense of the grading operator, ∗Talk given at the International Workshop “Supersymmetry and Quantum Symmetries”, JINR, Dubna, Russia, July 26-31,1999