Overview -- Theory of the Poincaré Group -- Theory of Spinors -- Group Contractions -- Covariant Harmonic Oscillator Formalism -- Dirac’s Form of Relativistic Quantum Mechanics -- Symmetries of Dirac’s Coupled Oscillators and Dirac’s Matrices -- The Lorentz Group -- Lorentz-Dirac Deformation in High-Energy Physics -- Decoherence and the Poincaré Sphere.-Lorentz Group in Classical Optics.

This book is intended mainly as a teaching tool directed toward those who desire a deeper understanding of group theory in terms of examples applicable to the physical world and/or of the physical world in terms of the symmetry properties which can best be formulated in terms of group theory. Both advanced students and scholars interested in the relationship between group theory and physics will find it instructive. In particular, those engaged in high-energy physics and foundations of quantum mechanics will find this book rich in illustrative examples of relativistic quantum mechanics. This new edition contains four new chapters, two of which are consistent with Dirac's aim to combine the important developments in physics in the twentieth century, namely quantum mechanics and special relativity. Moreover, these new chapters also discuss various aspects of classical and quantum optics that are now understood to be interrelated. Most of the original chapters have been updated, either with new material added or in some instances reinterpretation of the original. The order of the chapters has been rearranged to create a more cohesive presentation. The original purpose of the first edition, namely to present examples to which physics students and researchers can relate, has not been altered.