Geometric phases

Abstract

This is the first of two chapters covering the mathematical and theoretical preliminaries one needs to tackle the skyrmion problems. In particular, the materials of this chapter comprise fundamental aspects of the modern theory of magnetism. Nowadays, there exists a mostly uniform treatment of these topics across the many condensed matter theory books available. Despite the risk of banality, I have tried to include a self-contained chapter on the Berry phase for spin problems so that readers need not look elsewhere to garner the requisite background.