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 Poincare sphere on polarization optics.

Sibel Baskal, Middle East Technical University
Sibel Baskal is a Professor of Physics at the Middle East Technical University in Ankara, Turkey where she researches manifestations of Poincare, Lorentz, and Wigner's little groups and of group contractions in optical sciences. She also researches current problems in classical field theories such as sigma models, non-abelian gauge fields and general relativity, with a particular focus on alternative approaches.

Young S. Kim, University of Maryland
Young S. Kim is Professor Emeritus in the Department of Physics, University of Maryland. His research interests have focused on elementary particle theory, the foundations of quantum mechanics, and the Lorentz group applicable to other areas of physics including quantum optics, condensed matter physics, and classical mechanics.

Marilyn E. Noz, New York University School of Medicine
Marilyn E. Noz is a Research Professor and Professor Emerita in the Department of Radiology at the New York University School of Medicine. Her primary research focus is the integration of functional and anatomical (multi-modality) imaging into clinical practice. Image registration is used across multiple images, initially 2D, now 3D. Since 1971, her collaboration with Professor Kim in elementary particle physics has resulted in three books and more than 40 journal publications.

Table of Contents
1. The Lorentz Group and its Representations
2. Wigner's Little Groups for Internal Space-Time Symmetries
3. Two-by-two Representations of Wigner's Little Groups
4. One Little Group with Three Branches
5. Lorentz-covariant Harmonic Oscillators
6. Quarks and Protons in the Lorentz-covariant world
7. Coupled Oscillators and Squeezed States of Light
8. Lorentz Group in Ray Optics
9. Polarization Optics
10. Poincare Sphere