The structure of much of solid-state theory comes directly from group theory, but until now there has been no elementary introduction to the band theory of solids which adopts this approach. This book provides such an introduction, employing only the simplest and most basic of group theoretical ideas, and emphasizing the significance of symmetry in determining many of the essential concepts used in the subject. Topics include: the free-electron model, the reciprocal lattice and the Fourier series, space group representations, phonons and conductivity, and surface and impurity states, among...

This text presents a consistent description of the geometric and quaternionic treatment of rotation operators. Covers the fundamentals of symmetries, matrices, and groups and presents a primer on rotations and rotation matrices. Also explores rotations and angular momentum, tensor bases, the bilinear transformation, projective representations, more. Includes problems with solutions.

Mathematical truths are often so compelling that some mathematicians, scientists, and philosophers posit a purely nonmaterial realm of eternal truths accessible to the mind alone. Mathematical physicist Simon Altmann carefully criticizes this revival of a dualistic philosophy a la Plato in this highly stimulating book. Has mathematics and physics discovered a new supernatural world, or is this mental cosmos simply an outgrowth of natural evolutionary processes? This is the crucial philosophical issue that Altmann elucidates.

Altmann provides a thorough philosophical basis to understand the...