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Abstract

We develop a field-theoretical version of kinetic theory based on the pioneering work of Das and Mazenko. A canonical generating functional for correlators of macroscopic observables is derived using the language of path integrals with the microscopic phase-space coordinates as the fundamental variables determining the dynamics. The findings of the original works are generalised to systems with correlated initial conditions. An exact initial phase-space distribution for a homogeneous and isotropic Gaussian random field is calculated, translated into a diagram language and factorised into connected contributions. The grand canonical generating functional is derived for systems obeying statistical homogeneity and isotropy. Using this, a perturbation theory in terms of coupled integral equations is developed and shown to suffer from inconsistencies due to the presence of initial correlations. We discover hints at a possible cure by using the first order solution for two-point cumulants to reorganise one-loop diagrams. Applied to cosmological structure formation the first order solution for the density power spectrum is found to be the familiar linear growth solution. We argue why our approach should have superior performance in non-linear structure formation compared with the standard approach.