Differential Calculi on h-deformed Bosonic and Fermionic Quantum Planes

TL;DR

This paper explores differential calculus on h-deformed quantum spaces, revealing the structure of fermionic quantum space with parafermionic variables and establishing a link between classical and deformed su(2) algebras.

Contribution

It introduces a differential calculus framework on h-deformed bosonic and fermionic quantum planes, including the construction of classical and deformed su(2) algebras.

Findings

Fermionic quantum space includes parafermionic and classical fermionic variables.

Constructed classical su(2) algebra on fermionic quantum space.

Established a mapping between classical and h-deformed su(2) algebras.

Abstract

We study differential calculus on h-deformed bosonic and fermionic quantum space. It is shown that the fermionic quantum space involves a parafermionic variable as well as a classical fermionic one. Further we construct the classical $su(2)$ algebra on the fermionic quantum space and discuss a mapping between the classical $su(2)$ and the h-deformed $su(2)$ algebras.