Topological excitations in a condensate of nonrelativistic bosons coupled to Maxwell and Chern-Simons fields

Abstract

The Jackiw-Pi model of the self-gravitating gas of nonrelativistic bosons coupled to the Chern-Simons gauge field is known to exhibit asymptotically vanishing, lumplike soliton solutions. We show that in order to extend this model to include the case of repulsive gases where the matter field approaches nonzero values at infinities, one has to add, for instance, the background electric charge. Reformulating the model arising in this way as a constrained Hamiltonian system allows one to find the self-duality limit in the pure Chern-Simons and in the mixed Chern-Simons-Maxwell cases. We prove that the linear momentum of the topologically nontrivial configurations can only be defined as a translationally noninvariant quantity and the algebra is spontaneously broken: {${\mathit{P}}_{\mathit{x}}$,${\mathit{P}}_{\mathit{y}}$}=2\ensuremath{\pi}${\mathrm{\ensuremath{\rho}}}_{0}$n.