Construction of bosons and fermions out of quons

The quon algebra describes particles, "quons", that are neither fermions no r bosons, using a label q that parametrizes a smooth interpolation between bosons (q = 1) and fermions (q = -1). Understanding the relation of quons o n the one side and bosons or fermions on the other can shed light on the di fferent properties of these two kinds of operators and the statistics which they carry. In particular, local bilinear observables can be constructed f rom bosons and fermions, but not from quons. In this Letter we construct bo sons and fermions from quon operators. For bosons, our construction works f or -1 less than or equal to q less than or equal to 1. The case q = -1 is p aradoxical, since that case makes a boson out of fermions, which would seem to be impossible. Nonetheless, when the limit q --> -1 is taken from above , the construction works. For fermions, the analogous construction works fo r -1 less than or equal to q less than or equal to 1, which includes the pa radoxical case q = 1. (C) 2001 Elsevier Science B.V. All rights reserved.