Running surface couplings

We discuss the renormalization group improved effective action and running surface couplings in curved spacetime with boundary. Using scalar self-interacting theory as an example, we study the influence of boundary effects to the effective equations of motion in the spherical cap and the relevance of surface running couplings to quantum cosmology and the symmetry breaking phenomenon. Running surface couplings in the asymptotically free SU (2) gauge theory are found.