Nonperturbative Spontaneous Symmetry Breaking

One of the most astonishing results of quantum field theory is spontaneous symmetry breaking. One can say that it is the situation when something arises from the quantization. This means that on the quantum level one has something that was not present on the classical level. Coleman and Weinberg [1] write : “ . . . higher-order effects may qualitatively change the character of a physical theory . . . ”. The main goal of the Coleman-Weinberg mechanism is to derive a Higgs potential from more fundamental principles, with as few arbitrary parameters as possible. In this mechanism the Higgs potential is induced by radiative corrections, rather than being inserted by hand. In this approach one can summarize over higher-loop graphs to induce an effective potential, which may then produce spontaneous symmetry breaking. Of coarse, it can be only in the theories with interactions (where we have these higher-loop graphs) : i.e. a nonlinearity (in Lagrangian) can lead to the interesting consequences for quantized theory. It is not very surprisingly because on the classical level we have the same : very simple behavior of a classical linear theory can be changed on the very complicated and surprising behavior of a classical nonlinear theory.