Introduction

After Einstein's identification of the invariance group of space and time in 1905, symmetry principles received an enthusiastic welcome in physics, with the hope that these principles could express the simplicity of nature in its deepest level. Since 1927 [99,100], it has been recognized that Quantum ElectroDynamics (QED) has a local symmetry under the transformations in which the electron field has a phase change that can vary point to point in space–time, and the electromagnetic vector potential undergoes a corresponding transformation. This kind of transformation is called a U(1) gauge symmetry due to the fact that a simple phase change can be thought as a multiplication by a 1 × 1 unitary matrix. Largely motivated by the challenge of giving a field-theoretical framework to the concept of isospin invariance, Yang and Mills [101] in 1954 extended the idea of QED to the SU(2) group of symmetry. However, it appears here that the symmetry would have to be approximate because gauge invariance requires massless vector bosons like the photon, and it seems obvious that strong interactions of pions were not mediated by massless but by the massive ρ mesons. In 1961, there was the idea of dynamic breaking, i.e., the Hamiltonian and commutation relations of a quantum theory could possess an exact symmetry and the symmetry of the Hamiltonian might not turn to be a symmetry of the vacuum.