Evaluating the effective action

The use of effective field theory, in situations wherein the energy-momentu m of light particles is much lower than the rest mass of heavy degrees of f reedom, has become an important one in contemporary physics. Herein we exam ine various means by which this effective action can be evaluated, using th e effective photon-photon interaction-the Euler-Heisenberg Lagrangian-as a pedagogical example.