Applications of Effective Lagrangians

Effective Lagrangians were originally used only at the tree level as so-called phenomenological Lagrangians since they were in general non-renormalizable. Today they are treated as effective field theories valid below a characteristic energy scale. Quantum corrections can then be calculated in a consistent way as for any renormalizable theory. A few applications of the Euler-Heisenberg Lagrangian for interacting photons at low energies are presented together with recent developments in the use of QED for non-relativistic systems. Finally, the ingredients of an effective theory for the electroweak sector of the Standard Model are discussed in the case of a non-linear realization of the Higgs mechanism using the Stuckelberg formalism. [Invited talk at "Beyond the Standard Model V", Balholm, Norway, April 29 - May 4, 1997]