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The Galilean invariance of the Navier-Stokes equation is shown to be akin toa global gauge symmetry familiar from quantum field theory. This symmetry leadsto a multiple counting of infinitely many inertial reference frames in the pathintegral approach to randomly stirred fluids. This problem is solved by fixingthe gauge, i.e., singling out one reference frame. The gauge fixed theory hasan underlying Becchi-Rouet-Stora (BRS) symmetry which leads to the Wardidentity relating the exact inverse response and vertex functions. Thisidentification of Galilean invariance as a gauge symmetry is explored indetail, for different gauge choices and by performing a rigorous examination ofa discretized version of the theory. The Navier-Stokes equation is alsoinvariant under arbitrary rectilinear frame accelerations, known as extendedGalilean invariance (EGI). We gauge fix this extended symmetry and derive thegeneralized Ward identity that follows from the BRS invariance of thegauge-fixed theory. This new Ward identity reduces to the standard one in thelimit of zero acceleration. This gauge-fixing approach unambiguously shows thatGalilean invariance and EGI constrain only the zero mode of the vertex but noneof the higher wavenumber modes.

Gauge fixing, BRS invariance and Ward identities for randomly stirred flows