Noether Theorem and Symmetry Breaking

Abstract

The existence of sectors, i.e. of “disjoint physical worlds” in the set of solutions of the non-linear equation (4.6), provides the mathematical and physical basis for the mechanism of spontaneous symmetry breaking briefly discussed in Chap. 2. We can now understand the relation between the Noether theorem, the existence of conserved currents and the occurrence of spontaneous symmetry breaking, which, among other things, implies the lack of existence of the corresponding generators. As shown by the following Propositions, the mechanism of spontaneous symmetry breaking is related to the instability of a physical world under a symmetry operation.