DEFORMATION METHODS FOR SINGLE PARAOSCILLATOR SYSTEMS

The origin of and distinction between the two deformation techniques c urrently in use for single particle paraoscillators is made clear. For paraoscillators deformed using the more familiar method, algebra defo rmation, (i) a single deformation function:unifying parabosons and par afermions is provided and (ii) Fock space representations of all singl e paraoscillator systems as bilinear combinations of deformed oscillat ors are obtained. For the (distinct) Fock space deformation method, th e deformed paraoscillator algebras are worked out in detail and their Casimir operators are given. Difficulties concerning the relationship between the single particle Calogero-Vasiliev oscillator and the singl e particle parabose system are resolved. (C) 1995 American Institute o f Physics.