General relativity and matter: a spinor field theory from fermis to light-years

General Relativity and Matter......Page iii
ISBN 9027713812......Page iv
Table of Contents......Page v
Ed. Preface, A. van der Merwe......Page ix
Foreword, C. Kilmister......Page xi
Author\'s Preface......Page xv
Part A......Page p1
1.1. The Principle of Relativity......Page p3
1.2. Meaning of Motion in Relativity Theory......Page p6
1.3. Speed of Light... & Space-Time Fusion......Page p8
1.4. Continuity Replaces Atomism......Page p10
1.5. The Unified Field Concept......Page p11
1.6. General Relativity & Geometry......Page p14
1.7. A Generalized Mach Principle......Page p17
Part B: Mathematical Preliminaries......Page p20
2.1. The Invariant Metric......Page p21
2.2. Sp.R. Transformations, The Poincare Group......Page p22
2.4. The Covariant Vector Field......Page p25
2.6. Corresp. Contra- & Covariant V. Transformations in SR......Page p26
2.8. The Metric Tensor g-sub-mu-nu(x)......Page p27
2.9. The Inverse Metric Tensor Field......Page p28
2.10. Conversion between Contra- & Covariant Tensor Indices......Page p29
2.11. Transformation Properties of Volume in GR......Page p30
2.12. Calc. Vector & Tensor Fields in Riemannian Space-Time......Page p31
2.13. Covariant Derivative, General Properties......Page p33
2.14. Deriv. Affine Connection from Metric Tensor......Page p35
2.15. The Geodesic Equation......Page p36
3.1. Discovery of Spinors in Physics......Page p40
3.2. The Algebra of Complex Numbers......Page p41
3.3. Group Properties of Complex Numbers......Page p43
3.4. The Algebra of Quaternions......Page p44
3.6. The Spinor Field & Special Relativity......Page p49
3.7. Transformation Props. of Spinor......Page p52
3.8. Explicit Spinor Reps. of Poincare Group......Page p53
3.9. 3-Dim. Rotation Group & Spinor Transformations......Page p54
3.10. Lack of Reflection Symmetry in Spinor Form.......Page p55
3.11. Spinors & Quaternions in Riemannian Space-Time......Page p57
3.12. Conjugation, T-Rev. of Spinor & Quaternion Fields......Page p61
3.13. Quaternion Calculus......Page p62
3.14. Spin-Affine Connection......Page p64
3.15. Spinor Transformations in GR......Page p66
Part C: The Field Equations......Page p71
4.1. Origin of Inertia & Mach\'s Principle......Page p73
4.2. Matter F. Eqns. from Quaternion Calculus in SR......Page p77
4.3. Relativistic Covariance......Page p79
4.4. The Bispinor Form of Dirac Equation......Page p80
4.5. Inertial Mass Field from General Relativity......Page p82
4.6. The Matter Field Equations in GR......Page p85
4.7. Gauge Invariance......Page p86
4.8. Electromagnetic Coupling......Page p90
4.9. The Null Electromagnetic Potential......Page p91
4.11. QM limit of the Matter Field Equations......Page p92
4.12. Energy and Momentum Operators......Page p95
4.13. Unification: Inertia, Grav., E-magnetism......Page p96
4.14. Mass Spectrum of Elementary Matter......Page p97
5.1. Generalized Mach Pr. in E-m Theory, Implications......Page p99
5.2. Vector-Tensor formns of Maxwell\'s Equations in SR......Page p103
5.3. Genlz. Maxwell\'s Eqns, Elementary Interaction Formalism......Page p106
5.4. Conventional Forms of Maxwell\'s Equations in GR......Page p108
5.5. A Spinor Formulation of E-m theory in SR......Page p110
5.6. Invariants & Conservation Laws......Page p113
5.7. Lagrangian for Spinor Form. of Electromagnetism......Page p115
5.8. Solutions of Spinor Field Equations......Page p117
5.9. Spinor Field Soln., Static Point Charge......Page p119
5.10. Coulomb\'s Law......Page p120
5.12. Global Extension of Spinor Conservation Laws......Page p124
5.13. E-m Interaction Functional in Matter Field Equations......Page p128
6.1. Physics, Geometry, & Algebra......Page p132
6.2. Toward a Unified Field Theory......Page p134
6.3. Einstein\'s Field Eqns & the Mach Principle......Page p137
6.4. The Riemann Curvature Tensor......Page p139
6.5. The Ricci Tensor......Page p140
6.6. The Einstein Field Equations......Page p141
6.7. Planetary Motion & Schwarzschild Problem......Page p142
6.8. The Newtonian Limit......Page p144
6.9. The Gravitational Red Shift......Page p146
6.10. Precession of Perihelion of Planetary Orbit......Page p148
6.11. The Bending of Light......Page p150
6.12. Variables of Riemannian Space-Time in Quaternion Form......Page p151
6.13. Least-Action Derivation, Quaternion Metrical F.E.......Page p153
6.14. Symm/Antisymm. Tensor Representation of GR......Page p156
6.14.1. Einstein\'s F.Eqns. from Symmetric Tensor Part......Page p157
6.14.2. Maxwell\'s F.E. from Antisymmetric Tensor Part......Page p159
6.15. Quantization of E. Charge in GR......Page p164
6.16. Mass Doublets from General Relativity......Page p167
6.17. A Linear Approximation......Page p168
6.18. The Electron-Muon Mass Doublet......Page p170
6.19. Lifetime of the Muon......Page p174
7.1. Introduction......Page p177
7.2. The Geodesic Equation in Quaternion Form.......Page p178
7.3. Planetary Motion from Quaternion Form. of GR......Page p182
7.4. Appl. to the Schwarzschild Problem......Page p184
7.5. Cf. Quaternion, Classical, & Tensor Predictions of Planetary Motion......Page p185
7.6. The Radial Solutions & Perihelion Precession......Page p187
7.7. Implications of the Hubble Law & the Expanding Universe......Page p189
7.8. The Spiral Structures of Galaxies......Page p193
7.9. Conclusions......Page p197
Bibliography......Page p201
Selected Author\'s Bibliography......Page p202
Index......Page p204
back......Page p210
Ref. [4]......Page p522