  Lecture Notes for Les Houches 2018 Summer School on Active Matter and
Nonequilibrium Statistical Physics. These notes give an introduction to
statistical field theories of active matter. After showing an example of how
such theories can be created bottom-up by explicit coarse graining of active
particle models, the main approach taken here is top-down: minimal terms are
added to well-studied stochastic field theories of passive systems that break
time-reversibility and thereby cause nonzero steady-state entropy production.
These theories are, so far, rather poorly understood compared to their passive
counterparts.
