Gradient Expansion in Conformal Relativistic Fluids

The quark-gluon plasma (QGP) is a very high-energy relativistic fluid that existed near the beginning of the universe. It is key in understanding what the universe was like at very early times, right after the big bang. Since it exists at such high energies, Einstein's theory of general relativity must be used to describe its dynamics. The QGP is also thought to be a conformal, or massless, fluid. Therefore, understanding the physics of conformal relativistic fluids has important applications in particle physics. In this presentation, I will present our work in the development of the mathematical formulation of these fluids via the energy-momentum tensor. Our approach has two novel features: Firstly, we prove a completeness theorem asserting that the gradient expansion can be carried out using Weyl derivatives, which transform homogeneously under conformal transformation. Secondly, we develop a novel diagrammatic approach to systematically write the gradient expansion of the energy-momentum tensor at arbitrary order using graphs.