Introduction

Abstract

In the history of physics, the cooperation of physicists and mathematicians has yielded great harvest in the first half of the twentieth century, as the installation of group theory in quantum mechanics (Weyl 1950). One of the main applications is realized in the field of solid-state physics (Inui et al. 1990; Tinkham 2003; Dresselhaus 2008). In subsequent years, however, such productive relationship between physics and mathematics became enfeebled, as physicists and mathematicians were pursuing their own interests separately. In material science, the typical tool of study has turned into “first principle electronic structure computation”, in which rapid computers are intensively used so that the quantitative simulation could be achieved. In contrast, the group theoretical view in the quantum physics is rather a qualitative one, which could explain the likeness in similar material structures, but could not illuminate the origin of subtle but distinct differences. The standpoints of group theoretical analysis, and of first principles simulation, are located at cross-purposes. This is one of the reasons which brought about the breaking-off between the group theory and the first principles electronic structure computation.