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The role of Weyl symmetry in hydrodynamics. (English) Zbl 1383.76557
Summary: This article is dedicated to the analysis of Weyl symmetry in the context of relativistic hydrodynamics. Here, we discuss how this symmetry is properly implemented using the prescription of minimal coupling: $$\partial \rightarrow \partial + \omega \mathcal{A}$$ . 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 hydrodynamics, 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 freedom, shear, vorticity and the metric tensor, are see in this context as charged fields under the Weyl gauge connection. The gauge nature of the connection provides natural dynamics to it via equations of motion analogous to the Maxwell equations for electromagnetism. As a consequence, a charge for the Weyl connection is defined and the notion of local charge is analyzed generating the conservation law for the Weyl charge.

##### MSC:
 76Y05 Quantum hydrodynamics and relativistic hydrodynamics 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) 70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
##### Keywords:
Weyl symmetry; general relativity; gauge theory; hydrodynamics
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