Deformed exterior algebra, Quons and related Coherent States

TL;DR

This paper reviews deformed exterior algebra and its relation to generalized statistics, focusing on quons, and discusses methods for constructing coherent states for deformed oscillators with numerous examples.

Contribution

It introduces a unified approach to deforming exterior algebra and explores the construction of coherent states for deformed oscillators, including quons.

Findings

Deformation of exterior algebra over vector spaces and manifolds.

Relation of deformed algebra to generalized statistics and quons.

Comprehensive review of methods for constructing 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.