  Vortices in a Bose-Einstein condensate are modelled as spontaneously symmetry
breaking minimum energy solutions of the time dependent Gross-Pitaevskii
equation, using the method of constrained optimization. In a non-rotating
axially symmetric trap, the core of a single vortex precesses around the trap
center and, at the same time, the phase of its wave function shifts at a
constant rate. The precession velocity, the speed of phase shift, and the
distance between the vortex core and the trap center, depend continuously on
the value of the conserved angular momentum that is carried by the entire
condensate. In the case of a symmetric pair of identical vortices, the
precession engages an emergent gauge field in their relative coordinate, with a
flux that is equal to the ratio between the precession and shift velocities.
