Deformed $C_{\lambda}$-Extended Heisenberg Algebra in Non-commutative Phase-Space

TL;DR

This paper constructs a deformed algebra in non-commutative phase space that models exotic particles interpolating between bosons and fermions, revealing new symmetry structures.

Contribution

It introduces a novel deformed $C_{}$-extended Heisenberg algebra in non-commutative space, capturing exotic particle statistics.

Findings

Defines a new algebraic structure for exotic particles

Shows the algebra interpolates between bosonic and fermionic cases

Provides a framework for symmetry analysis in non-commutative quantum systems

Abstract

We construct a deformed $C_{\lambda}$-extended Heisenberg algebra in two-dimensional space using non-commuting coordinates which close an algebra depends on statistical parameter characterizing exotic particles. The obtained symmetry is nothing but an exotic particles algebra interpolating between bosonic and deformed fermionic algebras.