2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/52790The 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 $ν$ and the dimension of space. The anyonic algebra \cite{upa} is recalled as a deformed Heisenberg algebra and a deformed $C_λ$-extended Heisenberg algebra.7 pages, clarifications, references added, Presented in the XIIIth Oporto Meeting on Geometry, Topology And Physics, Oporto, Portugal (2004)High Energy Physics - Theorytext