Group Theory: Application to the Physics of Condensed Matter

This concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters.

[from the Preface] Symmetry can be seen as the most basic and important concept in physics. Momentum conservation is a consequence of translational symmetry of space. More generally, every process in physics is governed by selection rules that are the consequence of symmetry requirements. On a given physical system, the eigenstate properties and the degeneracy of eigenvalues are governed by symmetry considerations. The beauty and strength of group theory applied to physics resides in the transformation of many complex symmetry operations into a very simple linear algebra. The concept of representation, connecting the symmetry aspects to matrices and basis functions, together with a few simple theorems, leads to the determination and understanding of the fundamental properties of the physical system, and any kind of physical property, its transformations due to interactions or phase transitions, are described in terms of the simple concept of symmetry changes.