Quantum dynamics of a vortex pair is investigated by considering the pair Hamiltonian within various, unequivalent algebraic frameworks. First the vortex pair spectrum is constructed in the standard contest of the $e\left(2\right)\mathrm{}$-like dynamical symmetry and its degeneracy is thoroughly examined. Then Berry’s phase phenomenon is studied through an $\mathrm{su}\mathrm{}(1,1)\mathrm{}$ realization of the pair Hamiltonian when its parameters are assumed to be time dependent, whereas the Feynman-Onsager quantization conditions are recovered by means of symmetry arguments within a third approach based on a magneticlike description of the vortex pair. Finally, it is shown how recasting the dynamical algebra in terms of two-particle realizations of both $\mathrm{su}\mathrm{}\left(2\right)\mathrm{}$ and $\mathrm{su}\mathrm{}(1,1)\mathrm{}$ provides the correct approach for the quantization of the model Hamiltonian accounting for the pair scattering from a disklike obstacle.

• Received 6 August 1998

DOI:https://doi.org/10.1103/PhysRevB.59.7127