Cohomological techniques based on BRST symmetry have proved invaluable for classifying consistent interactions in gauge theories. In this talk I will describe the application of this idea to massive field theories, which are made gauge invariant by the introduction of Stueckelberg fields. We illustrate the power of the method with two models: (1) starting with a collection of free massive vectors, we show how the method reproduces the cubic and quartic interaction vertices of massive Yang-Mills theory; (2) similarly, starting with a free massive graviton, we are able to recover the consistent cubic vertices of ghost-free massive gravity. The formalism further sheds light on the characterization of Stueckelberg theories, by demonstrating for instance that the gauge algebra of such models is Abelian and that they admit a so-called Born-Infeld formulation in which the action is constructed out of gauge-invariant structures.
