In this work we treat diffusion with the modern tools of effective field theory. We first present the Schwinger-Keldysh formalism for evaulating real-time correlators, study their properties and then use the insights gained to formulate an effective description of microscopic systems via the path integral formalism. We analyze the theory so obtained, first in broad strokes – for example, we prove the so-called largest time equation at the perturbative level – and then quantitatively. We determine the general form of the effetive action at first derivative order but at all orders in fields, then perturbatively compute the one-loop corrections and classify all two-loop diagrams.
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