Ward Identities for N=2 Rigid and Local Supersymmetry in Euclidean Space

We construct and check by explicit Feynman diagram calculations the BRST Ward identities for N=2 rigid super Yang-Mills theory and N=2 extended supergravity in four-dimensional Euclidean space without auxiliary fields. We use the Batalin-Vilkovisky formalism. In the supergravity case we need one new contractible pair of complex spinor fields to obtain the usual gauge-fixing term and corresponding Nielsen-Kallosh ghosts.