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

General Relativity and Matter......Page iii
ISBN 9789401576666......Page iv
Table of Contents......Page v
Preface, A. van der Merwe......Page ix
Foreword, C. Kilmister......Page xi
Author's Preface......Page xv
Part A......Page 1.djvu
1.1. The Principle of Relativity......Page 3.djvu
1.2. Meaning of Motion in Relativity Theory......Page 6.djvu
1.3. Speed of Light... & Space-Time Fusion......Page 8.djvu
1.4. Continuity Replaces Atomism......Page 10.djvu
1.5. The Unified Field Concept......Page 11.djvu
1.6. General Relativity & Geometry......Page 14.djvu
1.7. A Generalized Mach Principle......Page 17.djvu
Part B: Mathematical Preliminaries......Page 19.djvu
2.1. The Invariant Metric......Page 21.djvu
2.2. Sp.R. Transformations, The Poincare Group......Page 22.djvu
2.4. The Covariant Vector Field......Page 25.djvu
2.6. Corresp. Contra- & Covariant V. Transformations in SR......Page 26.djvu
2.8. The Metric Tensor g-sub-mu-nu(x)......Page 27.djvu
2.9. The Inverse Metric Tensor Field......Page 28.djvu
2.10. Conversion between Contra- & Covariant Tensor Indices......Page 29.djvu
2.11. Transformation Properties of Volume in GR......Page 30.djvu
2.12. Calc. Vector & Tensor Fields in Riemannian Space-Time......Page 31.djvu
2.13. Covariant Derivative, General Properties......Page 33.djvu
2.14. Deriv. Affine Connection from Metric Tensor......Page 35.djvu
2.15. The Geodesic Equation......Page 36.djvu
3.1. Discovery of Spinors in Physics......Page 40.djvu
3.2. The Algebra of Complex Numbers......Page 41.djvu
3.3. Group Properties of Complex Numbers......Page 43.djvu
3.4. The Algebra of Quaternions......Page 44.djvu
3.6. The Spinor Field & Special Relativity......Page 49.djvu
3.7. Transformation Props. of Spinor......Page 52.djvu
3.8. Explicit Spinor Reps. of Poincare Group......Page 53.djvu
3.9. 3-Dim. Rotation Group & Spinor Transformations......Page 54.djvu
3.10. Lack of Reflection Symmetry in Spinor Form.......Page 55.djvu
3.11. Spinors & Quaternions in Riemannian Space-Time......Page 57.djvu
3.12. Conjugation, T-Rev. of Spinor & Quaternion Fields......Page 61.djvu
3.13. Quaternion Calculus......Page 62.djvu
3.14. Spin-Affine Connection......Page 64.djvu
3.15. Spinor Transformations in GR......Page 66.djvu
Part C: The Field Equations......Page 71.djvu
4.1. Origin of Inertia & Mach's Principle......Page 73.djvu
4.2. Matter F. Eqns. from Quaternion Calculus in SR......Page 77.djvu
4.3. Relativistic Covariance......Page 79.djvu
4.4. The Bispinor Form of Dirac Equation......Page 80.djvu
4.5. Inertial Mass Field from General Relativity......Page 82.djvu
4.6. The Matter Field Equations in GR......Page 85.djvu
4.7. Gauge Invariance......Page 86.djvu
4.8. Electromagnetic Coupling......Page 90.djvu
4.9. The Null Electromagnetic Potential......Page 91.djvu
4.11. QM limit of the Matter Field Equations......Page 92.djvu
4.12. Energy and Momentum Operators......Page 95.djvu
4.13. Unification: Inertia, Grav., E-magnetism......Page 96.djvu
4.14. Mass Spectrum of Elementary Matter......Page 97.djvu
5.1. Generalized Mach Pr. in E-m Theory, Implications......Page 99.djvu
5.2. Vector-Tensor formns of Maxwell's Equations in SR......Page 103.djvu
5.3. Genlz. Maxwell's Eqns, Elementary Interaction Formalism......Page 106.djvu
5.4. Conventional Forms of Maxwell's Equations in GR......Page 108.djvu
5.5. A Spinor Formulation of E-m theory in SR......Page 110.djvu
5.6. Invariants & Conservation Laws......Page 113.djvu
5.7. Lagrangian for Spinor Form. of Electromagnetism......Page 115.djvu
5.8. Solutions of Spinor Field Equations......Page 117.djvu
5.9. Spinor Field Soln., Static Point Charge......Page 119.djvu
5.10. Coulomb's Law......Page 120.djvu
5.12. Global Extension of Spinor Conservation Laws......Page 124.djvu
5.13. E-m Interaction Functional in Matter Field Equations......Page 128.djvu
6.1. Physics, Geometry, & Algebra......Page 132.djvu
6.2. Toward a Unified Field Theory......Page 134.djvu
6.3. Einstein's Field Eqns & the Mach Principle......Page 137.djvu
6.4. The Riemann Curvature Tensor......Page 139.djvu
6.5. The Ricci Tensor......Page 140.djvu
6.6. The Einstein Field Equations......Page 141.djvu
6.7. Planetary Motion & Schwarzschild Problem......Page 142.djvu
6.8. The Newtonian Limit......Page 144.djvu
6.9. The Gravitational Red Shift......Page 146.djvu
6.10. Precession of Perihelion of Planetary Orbit......Page 148.djvu
6.11. The Bending of Light......Page 150.djvu
6.12. Variables of Riemannian Space-Time in Quaternion Form......Page 151.djvu
6.13. Least-Action Derivation, Quaternion Metrical F.E.......Page 153.djvu
6.14. Symm/Antisymm. Tensor Representation of GR......Page 156.djvu
6.14.1. Einstein's F.Eqns. from Symmetric Tensor Part......Page 157.djvu
6.14.2. Maxwell's F.E. from Antisymmetric Tensor Part......Page 159.djvu
6.15. Quantization of E. Charge in GR......Page 164.djvu
6.16. Mass Doublets from General Relativity......Page 167.djvu
6.17. A Linear Approximation......Page 168.djvu
6.18. The Electron-Muon Mass Doublet......Page 170.djvu
6.19. Lifetime of the Muon......Page 174.djvu
7.1. Introduction......Page 177.djvu
7.2. The Geodesic Equation in Quaternion Form.......Page 178.djvu
7.3. Planetary Motion from Quaternion Form. of GR......Page 182.djvu
7.4. Appl. to the Schwarzschild Problem......Page 184.djvu
7.5. Cf. Quaternion, Classical, & Tensor Predictions of Planetary Motion......Page 185.djvu
7.6. The Radial Solutions & Perihelion Precession......Page 187.djvu
7.7. Implications of the Hubble Law & the Expanding Universe......Page 189.djvu
7.8. The Spiral Structures of Galaxies......Page 193.djvu
7.9. Conclusions......Page 197.djvu
Bibliography......Page 201.djvu
Selected Author's Bibliography......Page 202.djvu
Index......Page 204.djvu