Anyons on the sphere: analytic states and spectrum

Stephane Ouvry (1) , Alexios P. Polychronakos

1 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

We analyze the quantum mechanics of anyons on the sphere in the presence of a constant magnetic field. We introduce an operator method for diagonalizing the Hamiltonian and derive a set of exact anyon energy eigenstates, in partial correspondence with the known exact eigenstates on the plane. We also comment on possible connections of this system with integrable systems of the Calogero type.

Mots clés: magnetic field: constant; anyon; sphere; quantum mechanics; energy eigenstate; integrability; Hamiltonian

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]; Physique Générale [physics.gen-ph]

Stephane Ouvry, Alexios P. Polychronakos. Anyons on the sphere: analytic states and spectrum. Nuclear Physics B, 2019, 949, pp.114797. ⟨10.1016/j.nuclphysb.2019.114797⟩. ⟨hal-02303026⟩