Symmetries and Their Breaking of Strong Interaction System

This article reviews concisely the symmetries and their breaking of strong interaction system. To establish the bridge between the abstract symmetry concept and principle in mathematics and the application in physics to reveal the underlying principle of strong interaction, we describe not only the abstract concept but also the realization of the unitary and other symmetries with the microscopic particles. We then describe the evolution of the strong interaction matter in the early universe in view of the symmetries and their breaking, especially on the dynamical generation of the observable mass(i.e., DCSB) and those of the strong and other interactions (gauge symmetry and breaking). We make also a survey of the symmetries and their breaking of nucleus, with concentration on the general methods of studying the many-body system in the symmetry point of view, the multi-particle shell model and the interacting boson approximation (IBM), the modes of nuclear collective motion and their evolution (i.e., nuclear shape phase transition). The survey intends to link the fundamental approaches with the practical investigations in the related frontiers of research properly and promptly.