Particle-vortex dynamics in noncommutative space

We study the problem of a charged particle in the presence of a uniform magnetic field plus a vortex in noncommutative planar space considering the two possible non-commutative extensions of the corresponding Hamiltonian, namely the 'fundamental' and the 'antifundamental' representations. Using a Fock space formalism we construct eigenfunctions and eigenvalues finding in each case half of the states existing in the ordinary space case. In the limit of θ→0 we recover the two classes of states found in ordinary space, relevant for the study of anyon physics. (author)