Quasi-Particles Hamiltonian
  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. 
Jamila Douari