Kinetic field theory of compact systems

Abstract The kinetic field theory is developed without assumptions of statistical homogeneity and isotropy. In a solvable toy model with short-ranged interactions, we compare first-order perturbation theory to an iterated mean-field approximation scheme. We show that the mean-field theory preserves the non-negativity of the configuration-space density-density correlator, so that it remains interpretable as a probability density, while also qualitatively capturing collapse dynamics, including analytic estimates of blow-up times. In a non-compact self-gravitating sheet model (GSM), MFT is shown to agree with certain analytically controlled aspects of the late-time dynamics, but ultimately breaks down on the collapse time scale. In a compact GSM, the first-order perturbation theory is shown to analytically reproduce critical phenomena. This work suggests a path toward convergence analysis of the mean-field approximation and applications to more complex inhomogeneous systems.