SCALE DEPENDENCE OF THE AVERAGE POTENTIAL AROUND THE MAXIMUM IN PHI-4 THEORIES

The average potential describes the physics at a length scale k-1 by averaging out the degrees of freedom with characteristic momenta larger than k. The dependence on k can be described by differential evolution equations. We solve these equations for the non-convex part of the potential around the origin in phi4 theories, in the phase with spontaneous symmetry breaking. The average potential is real and approaches the convex effective potential in the limit k --> 0. Our calculation is relevant for processes for which the shape of the potential at a given scale is important, such as tunneling phenomena or inflation.