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

TL;DR

This paper explores the invariance properties of nonlinear gauge potentials in quantum fluids, revealing conditions under which gauge and Galilean symmetries are preserved or broken, with implications for superfluid dynamics.

Contribution

It derives transformation laws for nonlinear gauge potentials under Galilean boosts and gauge transformations, showing when hydrodynamic equations remain invariant.

Findings

Hydrodynamic equations are form-invariant with external gauge functions.

Nonlinear gauge potentials cannot always be gauged away, affecting fluid pressure.

Galilean covariance can be restored with specific transformation rules for potentials.

Abstract

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