Introduction

Abstract

Physical systems in general possess symmetry properties. An essential point in the discussion of such systems is to find the relevant symmetries and to classify the properties or the states of the systems with respect to these symmetries. Group theory provides the mathematical tools for the description of symmetries. Within representation theory, methods are developed that allow classification of the physical states of a system with respect to the irreducible representations of the symmetry group.

… διò δὴ καὶ χώραυ ταῦτα ἄλλαἄλλην ἴσχειν, πρὶν καὶ τὸ πᾶν ἐξ αὐτῶν διακοσμηθὲν γενέσθαι. Καὶ τὸ μὲν δὴ πρὸ τούτου πάντα ταῦτ′εἶχεν ἀλόγως καὶ ἀμέτρως…. οὕτω δὴ τότε πεφυκότα ταῦτα πρῶτον διεσχηματίσατο εἶδεσί τε καὶ ἀριθμοῖς. Platon, Timaios, 53a, b