Hopf Structure and Green Ansatz of Deformed Parastatistics Algebras

TL;DR

This paper introduces a Hopf algebra framework for deformed parabose and parafermi algebras, enabling new Fock-like representations and a generalized Green ansatz for deformed parastatistics.

Contribution

It provides a natural Hopf algebra structure for deformed parastatistics algebras and constructs Fock-like representations using a noncocommutative coproduct.

Findings

Established Hopf structure for deformed parabose and parafermi algebras

Constructed Fock-like representations from deformed bose and fermi bases

Derived quadratic algebras defining the generalized Green ansatz

Abstract

Deformed parabose and parafermi algebras are revised and endowed with Hopf structure in a natural way. The noncocommutative coproduct allows for construction of parastatistics Fock-like representations, built out of the simplest deformed bose and fermi representations. The construction gives rise to quadratic algebras of deformed anomalous commutation relations which define the generalized Green ansatz.