Download or read book Unitary Representations of the Poincaré Group and Relativistic Wave Equations written by Y Ohnuki and published by World Scientific. This book was released on 1988-04-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to an extensive and systematic study on unitary representations of the Poincaré group. The Poincaré group plays an important role in understanding the relativistic picture of particles in quantum mechanics. Complete knowledge of every free particle states and their behaviour can be obtained once all the unitary irreducible representations of the Poincaré group are found. It is a surprising fact that a simple framework such as the Poincaré group, when unified with quantum theory, fixes our possible picture of particles severely and without exception. In this connection, the theory of unitary representations of the Poincaré group provides a fundamental concept of relativistic quantum mechanics and field theory. Contents:Introduction:Transformation and InvariancePoincaré Group and Free ParticlesLorentz Group:Double-Valued RepresentationsSpinor RepresentationsInfinitesimal TransformationsIrreducible Representations of the Poincaré Group:Translational TransformationsLorentz TransformationsLittle GroupsIrreducible RepresentationsUnitary Representations of Little Groups:Rotation GroupTwo-Dimensional Euclidean GroupLorentz GroupThree-Dimensional Lorentz GroupClassifications of Free ParticlesWigner Rotations:Particles with Finite MassParticles with Zero MassParticles with Imaginary MassAngular Momenta of Massless ParticlesCovariant Formalism I — Massive Particles:Particles with Spin ODirac ParticlesParticles with Higher SpinGeneralized Bargmann-Wigner Equationsγ MatricesDiscrete TransformationsOther Covariant FormalismsCovariant Formalism II — Massless Particles:Particles with Discrete SpinDiscrete TransformationsCovariant Inner ProductsParticles with Continuous SpinQuantized Fields:Quantum Theory of Matter WavesHarmonic OscillatorsScalar FieldsSpin and StatisticsPoincaré Group and Free Fields Readership: Theoretical physicists and mathematicians. Keywords:Relativistic Wave Equations;Poincare;Relativistic Pictures of Particles in Quantum Mechanics;Quantum Theory;Relativistic Quantum Field Theory;Lorentz Group;Unitary Representation;Wigner Rotations