The Dynamical Rearrangement of Symmetry and the Group Contraction

Abstract

It frequently happens that the observable manifestation of a symmetry differs from the basic form of the symmetry of the dynamics. This phenomenon is called the dynamical rearrangement of symmetry. The phenomenon of spontaneous breakdown of symmetries (or the creation of ordered states) is really the result of symmetry rearrangement caused by the presence of massless Quanta called Goldstone bosons. In other words, the symmetry is not lost in spontaneous breakdown, but is rearranged into a different form in observation.I),2) It has sometimes been speculated that the dynamical rearrangement of a simple or a semi-simple Lie group symmetry follows the course of a group contraction. 3 ),4)