Two approaches to fractional supersymmetrical quantum mechanics

Two complementary approaches of = 2 fractional supersymmetrical quantum mechanics of order k 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 k ‐fermionic degrees of freedom. As an illustration, a particular emphasis is put on the fractional supersymmetrical oscillator of order k. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003