Finite-temperature effective action and thermalization of perturbations

The effective action is computed for the λφ4-theory at finite temperature for small perturbations about a constant background field, using a generalized tadpole method. We find the complete effective action, including the real and imaginary parts, to all orders in derivatives and to order O(λ2). The solutions of the dispersion relations show that initial perturbations do not necessarily thermalize fast enough to be absent at the onset of phase transition. ((orig.))