Deformed exterior algebra, Quons and related Coherent States

Abstract

We review the notion of the deformation of the exterior wedge product. This allows us to construct the deformation of the algebra of exterior forms over a vector space and also over an arbitrary manifold. We relate this approach to the generalized statistics. we study quons, as a particular case of these generalized statistics. We also give their statistical properties. A large part of the work is devoted to the problem of constructing coherent states for the deformed oscillators. we give a review of all the approaches existing in the literature concerning this point and enforce it with many examples.