Michael Dütsch

The main idea in the Epstein--Glaser renormalization scheme (causal perturbation theory) is to replace the coupling constant by a test-function g. This makes it possible to require a causality condition for the scattering matrix S(g), which translates into a corresponding factorization condition for the time-ordered products. This condition determines them a far extent. Renormalization amounts to extension of distributions. We illustrate some renormalization methods in explicit examples, working with a new formalism in which the observables are not Fock space operators; instead they are obtained by deformation quantization of off-shell fields.