Critical effects in semiclassical scattering, in which the standard approximations break down, are associated with forward peaking, rainbows, glories, orbiting and resonances. Besides giving rise to beautiful optical effects in the atmosphere, critical effects have important applications in many areas of physics. However, their interpretation and accurate treatment is difficult. This book, based on the Elliott Montroll Lectures, given at the University of Rochester, deals with the theory of these critical effects. After a preliminary chapter in which the problem of critical effects is posed, the next three chapters on coronae, rainbows and glories are written so as to be accessible to a broader audience. The main part of the book then describes the results obtained from the application of complex angular momentum techniques to scattering by homogeneous spheres. These techniques lead to practically usable asymptotic approximations, and to new physical insights into critical effects. A new conceptual picture of diffraction, regarded as a tunnelling effect, emerges. The final two chapters contain brief descriptions of applications to a broad range of fields, including linear and nonlinear optics, radiative transfer, astronomy, acoustics, seismology, atomic, nuclear and particle physics.

In this book, the author aims to familiarise researchers and graduate students, in both physics and mathematics, with the application of non-associative algebras in physics. Topics covered by the author are wide-ranging to include algebras of observables in quantum mechanics, angular momentum and octonions, division algebra, triple-linear products and Yang–Baxter equations. The author also covers non-associative gauge theoretic reformulation of Einstein's general relativity theory and similar subjects. Much of the material found in this book is not available in other standard works. This book will be of interest to graduate students and research scientists in physics and mathematics.