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Full Description
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 Poincar sphere on polarization optics.
Contents
Lorentz group and its representations
Wigner's little groups for internal space-time symmetries
Two-by-two representations of Wigner's little groups
One little group with three branches
Lorentz-covariant harmonic oscillators
Quarks and protons in the Lorentz-covariant world
Coupled oscillators and squeezed states of light
Lorentz group in ray optics
Polarization optics
Poincar sphere
