Geometry of Quantum Theory

Available for the first time in soft cover, this book is a classic on the foundations of quantum theory. It examines the subject from a point of view that goes back to Heisenberg and Dirac, and whose definitive mathematical formulation is due to von Neumann. This view, which is essentially geometric, leads most naturally to the questions of symmetry that are at the basis of all attempts to understand the world of atoms and subatomic particles. The mathematical treatment of symmetry in quantum theory is based on the theory of group representations, and this book includes a self-contained treatment of the parts of this theory which are among the most useful in quantum physics.This is a book about the mathematical foundations of quantum theory. Its aim is to develop the conceptual basis of modern quantum theory from general principles using the resources and techniques of modern mathematics.§There are two aspects to this book. The first deals with the geometrical structure of the logic of quantum mechanics, which is very different from that of classical mechanics, and which has as its source the complementarity principle that goes back to Bohr and Heisenberg. The treatment builds on the approach of Von Neumann. The second aspect is that of symmetry which plays a much greater role in quantum mechanics than in classical mechanics. Symmetry in quantum theory manifests itself through unitary representations of the symmetry groups, and the book presents a systematic treatment which is adequate for all applications.§All the fundamental results are proved here: Wigner s theorem on quantum symmetries, the equivalence of wave and matrix mechanics, namely, the identity of the Schrodinger and the Heisenberg Dirac pictures of the quantum world, impossibility of a hidden variables explanation of quantum theory (Von Neumann Mackey Gleason theorem), classification of free relativistic particles through their mass and spin, the structure of quantum systems of many identical particles (bosons and fermions), and so on.§The reader of this book will be thoroughly prepared for studying modern theories such as gauge theories, quantum field theory, and super symmetry.