Autonomous Renormalization of Phi^4 in Finite Geometry

The autonomous renormalization of the O(N)-symmetric scalar theory is based on an infinite re-scaling of constant fields, whereas finite-momentum modes remain finite. The natural framework for a detailed analysis of this method is a system of finite size, where all non-constant modes can be integrated out perturbatively and the constant mode is treated by a saddle-point approximation in the thermodynamic limit. The calculation provides a better understanding of the properties of of the effective action and corroborates earlier findings concerning a heavy Higgs particle at about 2 TeV.