Physics Of The Lorentz Group

Physics of the Lorentz Group

This book explains the Lorentz mathematical group in a language familiar to physicists. While the three-dimensional rotation group is one of the standard mathematical tools in physics, the Lorentz group of the four-dimensional Minkowski space is still very strange to most present-day physicists. It plays an essential role in understanding particles moving at close to light speed and is becoming the essential language for quantum optics, classical optics, and information science. The book is based on papers and books published by the authors on the representations of the Lorentz group based on harmonic oscillators and their applications to high-energy physics and to Wigner functions applicable to quantum optics. It also covers the two-by-two representations of the Lorentz group applicable to ray optics, including cavity, multilayer and lens optics, as well as representations of the Lorentz group applicable to Stokes parameters and the Poincaré sphere on polarization optics.

Physics of the Lorentz Group

Representations of the Rotation and Lorentz Groups and Their Applications

This monograph on the description and study of representations of the rotation group of three-dimensional space and of the Lorentz group features advanced topics and techniques crucial to many areas of modern theoretical physics. Prerequisites include a familiarity with the differential and integral calculus of several variables and the fundamentals of linear algebra. Suitable for advanced undergraduate and graduate students in mathematical physics, the book is also designed for mathematicians studying the representations of Lie groups, for whom it can serve as an introduction to the general theory of representation. The treatment encompasses all the basic material of the theory of representations used in quantum mechanics. The two-part approach begins with representations of the group of rotations of three-dimensional space, analyzing the rotation group and its representations. The second part, covering representations of the Lorentz group, includes an exploration of relativistic-invariant equations. The text concludes with three helpful supplements and a bibliography.