Classical approaches to Higgs mechanism

Abstract

The standard approach to Higgs mechanism is based on the existence of unitary gauge but, unfortunately, it does not come from a coordinate change in the configuration space of the initial model and actually defines a new dynamical system. So, it is a questionable approach to the problem but it is shown here that the final result could still make sense as a Marsden-Weinstein reduced system. (This reduction can be seen as completely analogous to the procedure of obtaining the "centrifugal" potential in the classical Kepler problem.) It is shown that in the standard linearization approximation of the Coulomb gauged Higgs model geometrical constraint theory offers an explanation of the Higgs mechanism because solving of the Gauss law constraint leads to different physical submanifolds which are not preserved by the action of the (broken) global U(1) group.