wether the local gauge symmetry is permissible in the superfluid He-4 model along with the global one?

For instance, for the (critical) superfluid velocity such local gauge transformation presumably  must be of the shape

  v_s \to v_s+ (\hbar/m) n grad \lambda (r)

with m,-the helium mass,  an integer n and same distance r function  \lambda (r).

 

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