Quasi-Particles Hamiltonian

TL;DR

This paper explores the Hamiltonian formulation of anyons, analyzing how bosonic and fermionic Hamiltonians emerge as limits, and discusses the algebraic structures underlying anyonic systems.

Contribution

It introduces a framework connecting anyonic Hamiltonians with deformed algebraic structures, highlighting the algebraic foundations of anyonic quantum mechanics.

Findings

Bosonic and fermionic Hamiltonians are derived as limits of the anyonic Hamiltonian.

The paper recalls the algebraic structures of deformed Heisenberg and $C_ u$-extended Heisenberg algebras.

Provides a unified algebraic approach to describe anyonic systems.

Abstract

The anyonic Hamiltonian is quantum mechanically given and the bosonic and the fermionic Hamiltonians are found as extremes by discussing the cases of the statistical parameter $\nu$ and the dimension of space. The anyonic algebra \cite{upa} is recalled as a deformed Heisenberg algebra and a deformed $C_\lambda$-extended Heisenberg algebra.