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Il Nuovo Cimento B

Applications of topological *-algebras of unbounded operators to modified quons

Fabio Bagarello

Published May 1, 2002• 7 citations
OpenAlex

Abstract

In this paper we discuss some applications of topological *-algebras of unbounded operators to what we call Modified Quons (MQ). In particular, the existence of the thermodynamical limit for some models of free and interacting modified quons is proved in the same framework proposed by the author in a recent paper for ordinary bosons.

Related papers

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We prove that, for the quon algebra, which interpolates between the Bose and Fermi statistics and depends on a free parameter q,it is possible to build an su(2) irreducible representation. One of the consequences of this fact is that the quons couple via the same angular momentum coupling rules obeyed by ordinary bosons and fermions. 1 1

•Jan 1, 1999•0 citations
During the past 20 years a long series of papers concerning algebras of unbounded operators appeared in the literature, papers which, though being originally motivated by physical arguments, contain almost no physics at all. On the contrary the mathematical aspects of these algebras have been analyzed in many details and this analysis produced, up to now, the monographes [32] and [2]. Some physics appeared first in [28] and [31], in the attempt to describe systems with a very large (10 24 ) number of degrees of freedom, following some general ideas originally proposed in the famous Haag and Kastler’s paper, [27], on QM ∞ .
The momentum operator representation of nonrelativistic anyons is developed in the Chern-Simons formulation of fractional statistics. The connection between anyons and the qqq-deformed bosonic algebra is established.