Theory of the Electron: A Theory of Matter from START

Theory of the Electron: A Theory of Matter from START

-

English

Description

The electron has come to be a fundamental element in the analysis of physical aspects of nature. This book is devoted to the construction of a deductive theory of the electron, starting from first principles and using a simple mathematical tool, geometric analysis. Its purpose is to present a comprehensive theory of the electron to the point where a connection can be made with the main approaches to the study of the electron in physics. The introduction describes the methodology. Chapter 2 presents the concept of space-time-action relativity theory, and in chapter 3, the mathematical structures describing action are analyzed. Chapters 4, 5, and 6 deal with the theory of the electron in a series of aspects where the geometrical analysis is more relevant. Finally in chapter 7 the form of geometrical analysis used in the book is presented to elucidate the broad range of topics which are covered and the range of mathematical structures which are implicitly or explicitly included.

Subjects

Informations

Published by
Published 01 January 2001
Reads 6
EAN13 0306471329
License: All rights reserved
Language English

Legal information: rental price per page €. This information is given for information only in accordance with current legislation.

Report a problem
Contents
Preface Acknowledgments 1. INTRODUCTION 1. The Nature of a Physical Theory 2. The Development of the Theory 3. Some Methodological Considerations 2. SPACE–TIME–ACTION RELATIVITY THEORY 1. Motivation for the Use of Space–Time–Action Geometry 2. Space–Time to Space–Time–Action 2.1 Formal Presentation 3. The Representation of the START Geometry 4. The Kinetic Energy in START 5. Dynamical Principles 5.1 STA Trajectories 5.2 Gauge Freedom in START 5.3 The Mathematical Structure of General Relativity from START 5.4 Lagrangians 5.5 Phase Space 5.6 The Group of Symmetries in START 3. ACTION MATHEMATICAL STRUCTURES 1. Action 1.1 Carriers 1.2 The Density as the Basic Variable 1.3 Introducing Gauge Freedom for the Description of the Energy 1.4 The Relation to Standard DFT 1.5 Relation of Action Density Functional to Action Amplitude Mechanics 1.6 Description in Terms of Interacting Carrier Fields 1.7 The Induced Probabilistic Interpretation ofΨ
vii
xi xv 1 2 3 7 13 13 16 17 20 22 24 25 26
36 42 43 44 45 45 46 48
49 50
52 56 60
viii
1.8 Quantum Mechanics from START 62 1.9 Some Remarks about the Formalism 63 2. Curvature 63 3. Matter, Geometry and Minimal Trajectory Condition 66 4. Center of Mass Coordinates and Hamiltonian Formalism 71 4.1 Gauging of the Two Carriers System 74 4. THE THEORY OF THE ELECTRON 79 1. Carrier Fields with Elementary Trajectories in START 79 2. Gauge Free Description of an Energy Distribution 80 2.1 Gauging of the Description of the Distribution 83 2.2 The Electron Field as a Sum of Massless Fields 85 2.3 Electrodynamics 86 3. Theoretical Description of the Electron in START 86 3.1 Local Structure of the Action Density 87 4. Densities and Currents of the Electron 89 5. The Electroweak Interaction of the Electron Field 95 5.1 The Theory of the Neutrino 95 5.2 The Electroweak Interaction of the Electron and the Neutrino 96 6. F o rm u la tio n o f a T h e o ry o f E le m e n ta ry P a rtic le s fro m START 97 6.1 Introduction 97 6.2 Complex Space–Time Geometry 99 6.3 Chiral Symmetry in Complex Space–Time 99 6.4 Chiral Geometry Theory of Elementary Particles 100 6.5 Masses and Geometric Analysis 107 5. GEOMETRY AND THE ELECTRON 119 1. Introduction 119 2. Geometry and the Electron 122 2.1 Mapping: Spinor to/from Multivector 126 2.2 Spin, de Broglie Waves, and Mass 127 2.3 The 1929 Work of Fock and Ivanenko 129 2.4 The Discovery of the Multi vector Wave Function 132 2.5 On the Algebraic Dirac Equation 133 2.6 Appendix 139 6. ALGEBRAIC ANALYSIS OF THE ELECTRON THEORY 151 1. The Algebraic Solution of the Dirac Equation 151 2. Twistors and Carriers 153 2.1 Introduction 153 2.2 Massless Carriers 155 2.3 Massive Carriers 157 2.4 Equations of Motion 167 7. GEOMETRICAL ANALYSIS 179 1. Introduction 179
2.
3.
4.
5.
6. 7.
8.
9.
10.
Contents
ix
1.1 The Geometric Program 179 1.2 Analysis 184 1.3 The Multi185vector Algebra 1.4 Spinors and Twistors 189 1.5 Geometric Analysis 189 1.6 Successive Complexification 194 1.7 Representations of Geometries 195 The Example of Space–Time 195 2.1 Chiral Symmetry in Complex Space–Time 197 2.2 Degenerate Representations 197 2.3 Massless Wave Equations 198 2.4 Structural Consequences of Using a Complex Space– Time Algebra 198 Polynomial Algebras. Groups. Matrix Representations 200 3.1 The Pauli Groups 201 3.2 The Dirac Group 203 3.3 Relation between the Dirac and the Pauli Groups 204 Derivation Operators 206 4.1 The Derivation in Geometric Analysis 207 4.2 Geometric Derivative 209 Steps to Build a Complex Space(–Time) 210 5.1 Oneand Twodimensional Cases 211 5.2 Higher211Dimensional Cases 5.3 Embedding 213 Mapping Complex into Real Geometric Spaces 213 Linear Vector Transformations 214 7.1 Restricted Transformations 217 Ideals, Spinors, Twistors, and Beyond 218 8.1 Twistors as Geometric Objects 219 8.2 Representation of the Poincaré Group 223 8.3 Screws and Multivector Screws 226 8.4 Multi229vector Screw for the Electron Field Historical Notes about Geometric Algebra and Calculus 235 9.1 Nineteenth Century 235 9.2 Twentieth Century 237 9.3 Early Twenty First Century 238 Basic Definitions 238
References
Index
241
255