Local Spin-Gauge Symmetry of the Bose-Einstein Condensates in Atomic Gases

The Bose-Einstein condensates of alkali atomic gases are spinor fields with local “spin-gauge” symmetry. This symmetry is manifested by a superfluid velocity ${\mathbf{u}}_s$ (or gauge field) generated by the Berry phase of the spin field. In “static” traps, ${\mathbf{u}}_s$ splits the degeneracy of the harmonic energy levels, breaks the inversion symmetry of the vortex nucleation frequency ${\mathbf{\Omega }}_{c1\mathrm{}}$, and can lead to vortex ground states.