Symmetry: The Formalism

Abstract

In Chapters 8–10 we study the general theory of symmetry in science via the conceptual approach. That approach is the best for understanding the concepts involved in symmetry and the significance of symmetry in science. But the application of symmetry considerations in science, and especially quantitative applications, require a general symmetry formalism. That formalism is developed in the present chapter and in Chapters 5–7 following. Mathematical concepts presented in the preceding two chapters are used extensively. Our road to symmetry starts with a state space of a system and proceeds through transformation, transformation group, equivalence relation for a state space, symmetry transformation, and symmetry group. The quantification of symmetry is discyssed, and a special section is devoted to symmetry of quantum systems.