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.
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