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.

Chapters: The Physical Meaning of Poincaré Massless Representations; Massless Representations; Massless Fields are Different; How to Couple Massless and Massive Matter; The Behaviour of Matter in Fields; Geometrical Reasons for the Poincaré Group; Description of the Electromagnetic Field; The Equations Governing Free Gravitation; How Matter Determines Gravitational Fields; Nonlinearity and Geometry; Quantum Gravity.