  We present a predictive local field theory for the nonequilibrium dynamics of
interacting active Brownian particles with a spherical shape in two spatial
dimensions. The theory is derived by a rigorous coarse-graining starting from
the Langevin equations that describe the trajectories of the individual
particles. For maximal accuracy and generality of the theory, it includes
configurational order parameters and derivatives up to infinite order. In
addition, we discuss possible approximations of the theory and present reduced
models that are easier to apply. We show that our theory contains popular
models such as Active Model B + as special cases and that it provides explicit
expressions for the coefficients occurring in these and other, often
phenomenological, models. As a further outcome, the theory yields an analytical
expression for the density-dependent mean swimming speed of the particles. To
demonstrate an application of the new theory, we analyze a simple reduced model
of the lowest nontrivial order in derivatives, which is able to predict the
onset of motility-induced phase separation of the particles. By a linear
stability analysis, an analytical expression for the spinodal corresponding to
motility-induced phase separation is obtained. This expression is evaluated for
the case of particles interacting repulsively by a Weeks-Chandler-Anderson
potential. The analytical predictions for the spinodal associated with these
particles are found to be in very good agreement with the results of Brownian
dynamics simulations that are based on the same Langevin equations as our
theory. Furthermore, the critical point predicted by our analytical results
agrees excellently with recent computational results from the literature.
