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It is possible to formulate fluid dynamics in terms of group-valued variables. This is particularly suited to the cases where the fluid has non-Abelian charges and is coupled to non-Abelian gauge fields. We explore this formulation further in this paper. An action for a fluid of relativistic particles (with and without spin) is given in terms of the Lorentz and Poincar\'e (or de Sitter) groups. Considering the case of particles with flavor symmetries, a general fluid action which also incorporates all flavor anomalies is given. The chiral magnetic and chiral vorticity effects as well as the consequences of the mixed gauge-gravity anomaly are discussed.
Nair et al. (Tue,) studied this question.