Relativistic Quantum Mechanics (Fundamental Theories of Physics Book 180)

This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semi group evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. The full gauge invariance of the Stueckelberg-Schroedinger equation results in a 5D generalization of the usual gauge theories. A description of this structure and some of its consequences for both Abelian and non-Abelian fields are discussed. A review of the basic foundations of relativistic classical and quantum statistical mechanics is also given. The Bekenstein-Sanders construction for imbedding Milgrom's theory of modified spacetime structure into general relativity as an alternative to dark matter is also studied. Acknowledgments 6 Contents 8 1 Introduction and Some Problems Encountered in the Construction of a Relativistic Quantum Theory 10 1.1 States in Relativistic Quantum and Classical Mechanics 10 1.2 The Problem of Localization for the Solutions of Relativistic Wave Equations 12 2 Relativistic Classical and Quantum Mechanics 17 2.1 The Einstein Notion of Time 17 2.2 Classical Mechanics 26 2.3 The Quantum Theory 28 2.4 The Newton-Wigner Problem 30 2.5 The Landau-Peierls Problem 32 3 Spin, Statistics and Correlations 40 3.1 Relativistic Spin and the Dirac Representation 40 3.2 The Many Body Problem with Spin, and Spin-Statistics 49 3.3 Construction of the Fock Space and Quantum Field Theory 51 3.4 Induced Representation for Tensor Operators 54 4 Gauge Fields and Flavor Oscillations 58 4.1 Abelian Gauge Fields 58 4.2 Nonabelian Gauge Fields and Neutrino Oscillations 66 4.3 The Hamiltonian for the Spin 1 2 Neutrinos 72 4.4 CP and T Conjugation 74 5 The Relativistic Action at a Distance Two Body Problem 77 5.1 The Two Body Bound State for Scalar Particles 78 5.2 Some Examples 90 5.3 The Induced Representation 94 5.4 The Stueckelberg String 99 6 Experimental Consequences of Coherence in Time 103 6.1 General Problem of Coherence in Time 103 6.2 The Lindner Experiment 104 6.3 Experiment Proposed by Palacios et al. 116 7 Scattering Theory and Resonances 118 7.1 Foundations of Relativistic Scattering Theory 119 7.2 The S Matrix 121 7.3 Cross Sections 126 7.4 Two Body Partial Wave Analysis 127 7.5 Unitarity and the Levinson Theorem 130 7.6 Resonances and Semigroup Evolution 131 7.7 Lax Phillips Theory 134 7.8 Relativistic Lee-Friedrichs Model 142 8 Some Applications: The Electron Anomalous Moment, Invariant Berry Phases and the Spacetime Lattice 148 8.1 The Anomalous Moment of the Electron 149 8.2 Invariant Berry Phases 154 8.3 The Spacetime Lattice 158 9 Hamiltonian Map to Conformal Modification of Spacetime Metric: Kaluza-Klein and TeVeS 161 9.1 Dynamics of a Relativistic Geometric Hamiltonian System 162 9.2 Addition of a Scalar Potential and Conformal Equivalence 163 9.3 TeVeS and Kaluza-Klein Theory 167 9.4 The Bekenstein-Sanders Vector Field as a Gauge Field 169 9.5 Summary 176 10 Relativistic Classical and Quantum Statistical Mechanics and Covariant Boltzmann Equation 177 10.1 A Potential Model for the Many Body System 178 10.2 The Microcanonical Ensemble 179 10.3 Canonical Ensemble 183 10.4 Grand Canonical Ensemble 188 10.5 Relativistic Quantum Quantum Statistical Mechanics 191 10.6 Relativistic High Temperature Boson Phase Transition 195 10.7 Black Body Radiation 197 10.8 Manifestly Covariant Relativistic Boltzmann Equation 200 11 Discussion 205 References 207 Index 215 This Book Describes A Relativistic Quantum Theory Developed By The Author Starting From The E.c.g. Stueckelberg Approach Proposed In The Early 40s. In This Framework A Universal Invariant Evolution Parameter (corresponding To The Time Originally Postulated By Newton) Is Introduced To Describe Dynamical Evolution. This Theory Is Able To Provide Solutions For Some Of The Fundamental Problems Encountered In Early Attempts To Construct A Relativistic Quantum Theory. A Relativistically Covariant Construction Is Given For Which Particle Spins And Angular Momenta Can Be Combined Through The Usual Rotation Group Clebsch-gordan Coefficients. Solutions Are Defined For Both The Classical And Quantum Two Body Bound State And Scattering Problems. The Recently Developed Quantum Lax-phillips Theory Of Semigroup Evolution Of Resonant States Is Described. The Experiment Of Lindner And Coworkers On Interference In Time Is Discussed Showing How The Property Of Coherence In Time Provides A Simple Understanding Of The Results. The Full Gauge Invariance Of The Stueckelberg-schroedinger Equation Results In A 5d Generalization Of The Usual Gauge Theories. A Description Of This Structure And Some Of Its Consequences For Both Abelian And Non-abelian Fields Are Discussed. A Review Of The Basic Foundations Of Relativistic Classical And Quantum Statistical Mechanics Is Also Given. The Bekenstein-sanders Construction For Imbedding Milgrom's Theory Of Modified Spacetime Structure Into General Relativity As An Alternative To Dark Matter Is Also Studied. Introduction And Some Problems Encountered In The Construction Of A Relativistic Quantum Theory -- Relativistic Classical And Quantum Mechanics -- Spin, Statistics And Correlations -- Gauge Fields And Flavor Oscillations -- The Relativistic Action At A Distance Two Body Problem -- Experimental Consequences Of Coherence In Time -- Scattering Theory And Resonances -- Some Applications: The Electron Anomalous Moment, Invariant Berry Phases And The Spacetime Lattice -- Hamiltonian Map To Conformal Modification Of Spacetime Metric: Kaluza-klein And Teves -- Relativistic Classical And Quantum Statistical Mechanics, And Covariant Boltzmann Equation. By Lawrence P. Horwitz. Front Matter....Pages i-viii Introduction and Some Problems Encountered in the Construction of a Relativistic Quantum Theory....Pages 1-7 Relativistic Classical and Quantum Mechanics....Pages 9-31 Spin, Statistics and Correlations ....Pages 33-50 Gauge Fields and Flavor Oscillations....Pages 51-69 The Relativistic Action at a Distance Two Body Problem....Pages 71-96 Experimental Consequences of Coherence in Time....Pages 97-111 Scattering Theory and Resonances....Pages 113-142 Some Applications: The Electron Anomalous Moment, Invariant Berry Phases and the Spacetime Lattice....Pages 143-155 Hamiltonian Map to Conformal Modification of Spacetime Metric: Kaluza-Klein and TeVeS....Pages 157-172 Relativistic Classical and Quantum Statistical Mechanics and Covariant Boltzmann Equation....Pages 173-200 Discussion....Pages 201-202 Back Matter....Pages 203-214