Twisted N=2 supersymmetry with central charge and equivariant cohomology

We present an equivariant extension of the Them form with respect to a vector field action, in the framework of the Mathai-Quillen formalism, The associated Topological Quantum Field Theories correspond to twisted N = 2 supersymmetric theories with a central charge. We analyze in detail two different cases: topological sigma models and non-abelian monopoles on four-manifolds.