Relativity, Symmetry and the Structure of Quantum Theory, Volume 1: Galilean quantum theory

"The history of how quantum mechanics was developed is a fascinating one and underlies the focus of this book; namely, given the rules that the founders of quantum mechanics developed, is it possible to find principles that lead to the structure of quantum mechanics as it was historically formulated? This is the first book in a series of works considering what particular relativity is applicable to a given dynamical theory. The series considers Newton, Einstein, and de Sitter relativities, while this book examines the unitary irreducible representations of the Galilei group and see how they provide the framework for Galilean quantum theory."--Font no determinada Annotation Quantum theory is one of the most successful of all physical theories. Our everyday world is dominated by devices that function because of knowledge of the quantum world. Yet many, physicists and non-physicists alike, find the theory which explains the behavior of the quantum world baffling and strange. This book is the first in a series of three that argues that relativity and symmetry determine the structure of quantum theory. That is to say, the structure of quantum theory is what it is because of relativity and symmetry. There are different types of relativity, each leading to a particular type of quantum theory. This book deals specifically with what we call Newton relativity, the form of relativity built into Newtonian mechanics, and the quantum theory to which it gives rise, which we call Galilean (often misleadingly called non-relativistic) quantum theory. Key Features: Meaning and significance of the term of relativity; discussion of the principle of relativity. Relation of symmetry to relativity. Significance of the notion of representations of symmetry transformations in formulating a quantum theory. Representations of Galilean symmetry and how they lead to the most common form of quantum theory. Extension of Newtonian relativity to accelerating quantum systems and broadened quantum theory." Preface 6 Author biographies 9 Chapter 1 Introduction 10 Bibliography 17 Chapter 2 Newton relativity and one-particle Galilean quantum theory 18 2.1 Unitary representations of the Galilei group 21 2.2 Complete systems of commuting observables 32 Bibliography 36 Chapter 3 Non-inertial transformations, fictitious forces and the equivalence principle 38 Bibliography 50 Chapter 4 Multiparticle systems and interactions 52 Bibliography 59 Chapter 5 Internal symmetries 60 Chapter 6 Conclusion 63 Bibliography 67 Appendix A Transitive manifolds 68 Appendix B Irreducible representations of the Galilei group and the origin of mass and spin 71 Bibliography 85 Appendix C Decomposition of n-fold tensor products and Clebsch-Gordan coefficients 86 Bibliography 93 Preface -- Author biographies -- Introduction -- Newton relativity and one-particle Galilean quantum theory -- Unitary representations of the Galilei group -- Complete systems of commuting observables -- Non-inertial transformations, fictitious forces and the equivalence principle -- Multiparticle systems and interactions -- Internal symmetries -- Conclusion -- Appendices -- A. Transitive manifolds -- B. Irreducible representations of the Galilei group and the origin of mass and spin -- C. Decomposition of n-fold tensor products and Clebsch-Gordan coefficients.