Deformation methods for single paraoscillator systems

Abstract

The origin of and distinction between the two deformation techniques currently in use for single particle paraoscillators is made clear. For paraoscillators deformed using the more familiar method, algebra deformation, (i) a single deformation function unifying parabosons and parafermions is provided and (ii) Fock space representations of all single paraoscillator systems as bilinear combinations of deformed oscillators are obtained. For the (distinct) Fock space deformation method, the 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 single particle parabose system are resolved.

Lasing in para-Fermi class-B microring resonator arrays

“…reminiscent of the angular momentum algebra su(2) with the addition of a parity operator Π [39,40]. In this representation, the action of the algebra elements in terms of the 2p + 1…”