This book explains the Lorentz group in a language familiar to physicists, namely in terms of two-by-two matrices. While the three-dimensional rotation group is one of the standard mathematical tools in physics, the Lorentz group applicable to the four-dimensional Minkowski space is still very strange to most physicists. However, it plays an essential role in a wide swathe of physics and is becoming the essential language for modern and rapidly developing fields. The first edition was prim...

The Lorentz group, which is the underlying scientific language for modern optics, has most notably been used for understanding Einstein’s special relativity. By using a simplified approach of two-by-two matrices and Wigner functions, this book provides a basic and novel approach to classical and quantum optics, making these difficult subjects more transparent to the reader. Written by three experts in the field, Sibel Başkal, Young S Kim and Marilyn E Noz, this book will provide the reader...

Einstein's energy-momentum relation is applicable to particles of all speeds, including the particle at rest and the massless particle moving with the speed of light. If one formula or formalism is applicable to all speeds, we say it is 'Lorentz-covariant.' As for the internal space-time symmetries, there does not appear to be a clear way to approach this problem. For a particle at rest, there are three spin degrees of freedom. For a massless particle, there are helicity and gauge degrees ...