  Based on a methodological analysis of the effective action approach certain
conceptual foundations of quantum field theory are reconsidered to establish a
quest for an equation for the effective action. Relying on the functional
integral formulation of Lagrangian quantum field theory a functional integral
equation for the complete effective action is proposed which can be understood
as a certain fixed point condition. This is motivated by a critical attitude
towards the distinction artificial from an experimental point of view between
classical and effective action. While for free field theories nothing new is
accomplished, for interacting theories the concept differs from the established
paradigm. The analysis of this new concept is concentrated on gauge field
theories treating QED as the prototype model. An approximative approach to the
functional integral equation for the complete effective action of QED is
exploited to obtain certain nonperturbative information about the quadratic
kernels of the action. As particular application the approximative calculation
of the QED coupling constant $\alpha$ is explicitly studied. It is understood
as one of the characteristics of a fixed point given as a solution of the
functional integral equation proposed. Finally, within the present approach the
vacuum energy problem is considered and possible implications on the induced
gravity concept are contemplated.
