Two approaches to fractional supersymmetrical quantum mechanics

Abstract

AbstractTwo complementary approaches of 𝒩 = 2 fractional supersymmetrical quantum mechanics of order k are studied in this article. The first, based on a generalized Weyl–Heisenberg algebra Wk (which comprises the affine quantum algebra Uq(sl2) with qk = 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