This article is dedicated to the analysis of Weyl symmetry in the context of
relativistic hydrodynamics. Here is discussed how this symmetry is properly
implemented using the prescription of minimal coupling: βββ+ΟA. It is shown that this prescription has no problem to deal
with curvature since it gives the correct expressions for the commutator of
covariant derivatives.
In the hydrodynamics the Weyl gauge connection emerges from the degrees of
freedom of the fluid: it is a combination of the expansion and entropy
gradient. The remaining degrees of the fluid and the metric tensor are see in
this context as charged fields under the Weyl gauge connection. The gauge
nature of conformal hydrodynamics is emphasized and a charge for the Weyl
connection is defined. A notion of local charge and current densities are
considered and a local charge conservation law is reached.Comment: 13 page