RECURSIVELY MINIMALLY-DEFORMED OSCILLATORS

A recursive deformation of the boson commutation relation is introduce d. Each step consists of a minimal deformation of a commutator [a,a da gger]=f(k)(...;(n) over cap) into [a,a dagger](qk=1)=f(k)(...;(n) over cap), where ... stands for the set of deformation parameters that f(k ) depends on, followed by a transformation into the commutator [a,a da gger]=f(k+1)(...,q(k+1);(n) over cap) to which the deformed commutator is equivalent within the Fock space. Starting from the harmonic oscil lator commutation relation [a,a dagger]=1 we obtain the Arik-Coon and Macfarlane-Biedenharn oscillators at the first and second steps, respe ctively, followed by a sequence of multiparameter generalizations. Sev eral other types of deformed commutation relations related to the trea tment of integrable models and to parastatistics are also obtained. Th e ''generic'' form consists of a linear combination of exponentials of the number operator, and the various recursive families can be classi fied according to the number of free linear parameters involved, that depends on the form of the initial commutator. (C) 1996 American Insti tute of Physics.