From Physical Concept to Mathematical Structure

The text takes an innovative approach to theoretical physics. It surveys the field in a way that emphasizes perspective rather than content per se, and identifies certain common threads, both conceptual and methodological, which run through the fabric of the subject today. Starting from recognized physical concepts, it demonstrates how these have led to the mathematical structures used extensively in physical theory and displays the unity of basic physics seen from the viewpoint of the symmetries of nature as manifested in the sensorial properties of physical quantities and physical laws. The text focuses particularly on the linearity principle. A consideration of the description of physical events as viewed from difference reference frames leads on to a discussion of the concepts of tensors and tensor fields as well as the theory of groups and group representations. As the concept of tensors is developed and broadened into multidimensional spaces, examples from elasticity theory, quantum mechanics, and the structure of elementary particles are considered. The nature of linear theories is illustrated repeatedly, but special attention is given to quantum mechanics and special relativity. The text also introduces non-linear geometry, in the sense of both Gauss and Riemann, and considers Riemannian geometry more extensively, as a prelude to a brief introduction to general relativity. The ten main chapters contain references, footnotes, and problems to assist the reader to pursue any topic further. The volume can serve as a text or supplementary text in advanced undergraduate or graduate programs in theoretical physics and should also prove of interest to practicing physicists, mathematicians, and theoretical chemists and biologists.