Global U(1) symmetry
= Global U(1) symmetry
A global phase symmetry sends a complex field to $e^{i\alpha}\phi$ with the same constant real $\alpha$ everywhere. It is distinct from allowing a spacetime-dependent phase together with a compensating gauge-field transformation. A global phase symmetry can produce a conserved <Noether current> and, in an appropriate ordered mean-field state, a continuum of degenerate phase choices.