The role of Weyl symmetry in hydrodynamics

Abstract

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: $\partial \to \partial +\omega \mathcal{A}$. 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 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.

13 pages

References in corpus (3)

• Fourth order Weyl gravity
• Tutorial on Scale and Conformal Symmetries in Diverse Dimensions
• Electrodynamics and spacetime geometry I: Foundations

Cited by in corpus (6)

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• Third-order relativistic hydrodynamics: dispersion relations and transport coefficients of a dual plasma
• Higgs Potential from Weyl Conformal Gravity
• Weyl Symmetry in Stochastic Quantum Gravity
• Two theorems for the gradient expansion of relativistic hydrodynamics
• Planck Scale from Broken Local Conformal Invariance in Weyl Geometry