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We investigate certain invariance properties of quantum fluids subject to anonlinear gauge potential. In particular, we derive the covarianttransformation laws for the nonlinear potentials under a space-time Galileanboost and consider U(1) gauge transformations. We find that the hydrodynamiccanonical field equations are form-invariant in the case of external gaugefunctions, but not for nonlinear gauge functionals. Hence, nonlinear gaugepotentials are non-trivial potentials which may not be "gauged-away". Notably,for a 1D superfluid, attempting to do so generates the gauge-pressure of thefluid in the Hamiltonian density. Further, we investigate how the fieldequations transform under arbitrary Galilean transformations. We find that theimmediate lack of Galilean covariance is restored under a suitably chosentransformation rule set for the potentials, which is identical in form to thatof a Schr\"odinger particle coupled to external scalar and vector potentials.

Gauge transformations and Galilean covariance in nonlinear gauge-coupled quantum fluids