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The study of active soft matter has developed into one of the most rapidlygrowing areas of physics. Field theories, which can be developed either viaphenomenological considerations or by coarse-graining of a microscopic model,are a very useful tool for understanding active systems. Here, we provide adetailed review of a particular coarse-graining procedure, theinteraction-expansion method (IEM). The IEM allows for the systematicmicroscopic derivation of predictive field theories for systems of interactingactive particles. We explain in detail how it can be used for a microscopicderivation of active model B+, which is a widely used scalar active mattermodel. Extensions and possible future applications are also discussed.

How to derive a predictive active field theory: a step-by-step tutorial