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Modern optics is the physics of two-by-two matrices and harmonic oscillators. The one- and two-photon coherent states are based on the mathematics of harmonic oscillators. This comprehensive book examines the mathematical details of how two-by-two matrices, Wigner functions and the Lorentz group can be implemented in classical and quantum optics.

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, classi...