The Bose-Einstein condensates of alkali atomic gases are spinor fields
with local ''spin-gauge'' symmetry. This symmetry is manifested by a
superfluid velocity u(s), (or gauge field) generated by the Berry phas
e of the spin field. In ''static'' traps, u(s) splits the degeneracy o
f the harmonic energy levels, breaks the inversion symmetry of the vor
tex nucleation frequency Omega(cl), and can lead to vortex ground stat
es.