Resummation of Perturbation Series in Non-Equilibrium Scalar Field Theory

The general behaviour of perturbation series in non-equilibrium scalar field theory is analysed in some detail, with a particular emphasis on the ``pathological terms'', generated by multiple products of $\delta$-functions. Using an intuitive regularization method, it is shown that these terms give large contributions at all orders, even when considering small deviations from equilibrium. Fortunately, these terms can also be resummed and I give the general expressions for the resummed propagators in non-equilibrium scalar field theory, regardless of the size of deviations from equilibrium.