Two Approaches to Fractional Supersymmetrical Quantum Mechanics

摘要

Two complementary approaches of N = 2 fractional supersymmetrical quantum mechanics of order kappa are studied in this article. The first, based on a generalized Weyl-Heisenberg algebra W_k (which comprises the affine quantum algebra U_q (sl_2) with q~k = 1 as a special case), apparently contains solely one bosonic degree of freedom. The second uses generalized bosonic and kappa-fermionic degrees of freedom. As an illustration, a particular emphasis is put on the fractional supersymmetrical oscillator of order kappa.