Derivative expansions of the non-equilibrium effective action

New techniques for evaluating the closed time path effective action for non-equilibrium quantum fields are presented. A derivative expansion is performed using a proper time kernel. Applications relevant to the scalar field theory of thermal inflation are discussed and dissipation terms resummed. The effective action of the electromagnetic field is also considered. In this case the leading term can be related to the conductivity of a plasma and has a simple interpretation in terms of the classical Drude theory of conductivity. (C) 2002 Elsevier Science B.V. All rights reserved.