Perturbative renormalization of the semi-infinite massive scalar field theory

So far there has not been a rigorous proof of perturbative renormalization of the massive scalar field theory with a quartic self-interaction on a half-space. In this talk, we will discuss the renormalisation problem of this model using the Polchinski flow equations in the case of the Robin boundary condition. We present the considered action and set up the system of perturbative flow equations satisfied by the connected amputated Schwinger distributions (CAS). To establish bounds on the CAS, being distributions, they have to be folded first with test functions. We introduce a suitable class of test functions together with the tree structures that will be used in the bounds to be derived on the CAS. We state the inductive bounds on the Schwinger functions which, being uniform in the cutoff, directly lead to renormalizability. Joint work with Christoph Kopper.