λφ 4 non - equilibrium dynamics and kinetic field theory 1

Off-shellness and inhomogeneities in the non-equilibrium dynamics of the λϕ 4 model are studied. The non equilibrium field theory is developed in the Closed Time Path formalism, which is in turn reformulated as a kinetic field theory, in terms of a set of kinetic equations for the 2-point Green function, derived from a generalized effective action functional. We take into account all initial correlations up to the 4-point functions. It is shown that the model displays an SO(1,1) symmetry broken by interactions and initial conditions. The divergence of the corresponding Noether current is identified as a particle creation/annihilation density. The broken Ward-Takahashi relations for the SO(1,1) symmetry are derived. They constitute a set of generalized kinetic equations for the general n-point functions. Energy-momentum conservation is demonstrated to hold from the fully interacting transport equations, and we discuss the effect of a gradient expansion and its non-locality. As an application, we study an explicit realization of inhomogeneities and non-equilibrium conditions in the free field model, for which we give the general solution and analyze it in a particular case. The identification of the Casimir effect in our solution illustrates the intimate connection between inhomogeneities and off-shellness.