TY - JOUR

T1 - Gauge fixing, BRS invariance and Ward identities for randomly stirred flows

AU - Berera, Arjun

AU - Hochberg, David

PY - 2009/6/1

Y1 - 2009/6/1

N2 - The Galilean invariance of the Navier-Stokes equation is shown to
be akin to a global gauge symmetry familiar from quantum field theory.
This symmetry leads to a multiple counting of infinitely many inertial
reference frames in the path integral approach to randomly stirred
fluids. This problem is solved by fixing the gauge, i.e., singling out
one reference frame. The gauge fixed theory has an underlying
Becchi-Rouet-Stora (BRS) symmetry which leads to the Ward
identity relating the exact inverse response and vertex functions. This
identification of Galilean invariance as a gauge symmetry is explored in
detail, for different gauge choices and by performing a rigorous
examination of a discretized version of the theory. The
Navier-Stokes equation is also invariant under arbitrary
rectilinear frame accelerations, known as extended Galilean invariance
(EGI). We gauge fix this extended symmetry and derive the generalized
Ward identity that follows from the BRS invariance of the gauge-fixed
theory. This new Ward identity reduces to the standard one in the limit
of zero acceleration. This gauge-fixing approach unambiguously shows
that Galilean invariance and EGI constrain only the zero mode of the
vertex but none of the higher wavenumber modes.

AB - The Galilean invariance of the Navier-Stokes equation is shown to
be akin to a global gauge symmetry familiar from quantum field theory.
This symmetry leads to a multiple counting of infinitely many inertial
reference frames in the path integral approach to randomly stirred
fluids. This problem is solved by fixing the gauge, i.e., singling out
one reference frame. The gauge fixed theory has an underlying
Becchi-Rouet-Stora (BRS) symmetry which leads to the Ward
identity relating the exact inverse response and vertex functions. This
identification of Galilean invariance as a gauge symmetry is explored in
detail, for different gauge choices and by performing a rigorous
examination of a discretized version of the theory. The
Navier-Stokes equation is also invariant under arbitrary
rectilinear frame accelerations, known as extended Galilean invariance
(EGI). We gauge fix this extended symmetry and derive the generalized
Ward identity that follows from the BRS invariance of the gauge-fixed
theory. This new Ward identity reduces to the standard one in the limit
of zero acceleration. This gauge-fixing approach unambiguously shows
that Galilean invariance and EGI constrain only the zero mode of the
vertex but none of the higher wavenumber modes.

UR - http://www.scopus.com/inward/record.url?scp=62349095203&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2009.01.014

DO - 10.1016/j.nuclphysb.2009.01.014

M3 - Article

VL - 814

SP - 522

EP - 548

JO - Nuclear physics b

JF - Nuclear physics b

SN - 0550-3213

IS - 3

ER -