Two oscillators quantum groups and associated deformed coherent states

TL;DR

This paper constructs new classes of deformed quantum groups from two oscillators, derives their superalgebra structures, and introduces novel deformed coherent states with explicit eigenstates.

Contribution

It develops a method to generate deformed fermionic-bosonic quantum Hopf algebras and constructs associated deformed coherent states.

Findings

New classes of deformed quantum groups are formulated.

Explicit realization of deformed superalgebra generators is provided.

Eigenstates of the generalized deformed annihilator are computed.

Abstract

Starting from a faithful five-dimensional matrix representation of the group of two independent oscillators and applying the R-matrix method we generate some classes of deformed fermionic-bosonic quantum Hopf algebras. The corresponding Lie deformed superalgebras of type I--II, obtained by duality, are computed and a realization of generators of these deformed superalgebras are given in terms of the usual fermionic and bosonic creation and annihilation operators associated to the supersymmetric harmonic oscillator. Then, a generalized deformed annihilator is construted and their eigenstates are computed giving a new class of deformed coherent states.