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Abstract: I will introduce the Schwinger-Keldysh (SK) formalism for quantum many body systems. Then, following [arxiv: 1511.03646], explain how SK is used to derive an effective field theory (EFT) of hydrodynamics. Finally, as a concrete application of the EFT, I will discuss the results obtained in our paper [arxiv: 1811.12540] for diffusive fluctuations.