Space-time Symmetry And Quantum Yang-mills Gravity: How Space-time Translational Gauge Symmetry Enables The Unification Of Gravity With Other Forces

by Jong-ping Hsu, Leonardo Hsu

Overview

Yang-Mills gravity is a new theory, consistent with experiments, that brings gravity back to the arena of gauge field theory and quantum mechanics in flat space-time. It provides solutions to long-standing difficulties in physics, such as the incompatibility between Einstein's principle of general coordinate invariance and modern schemes for a quantum mechanical description of nature, and Noether's ‘Theorem II’ which showed that the principle of general coordinate invariance in general relativity leads to the failure of the law of conservation of energy. Yang-Mills gravity in flat space-time appears to be more physically coherent than conventional gravity in curved space-time. The problems of quantization of the gravitational field, the operational meaning of space-time coordinates and momenta, and the conservation of energy-momentum are all resolved in Yang-Mills gravity.The aim of this book is to provide a treatment of quantum Yang-Mills gravity, with an emphasis on the ideas and evidence that the gravitational field is the manifestation of space-time translational symmetry in flat space-time, and that there exists a fundamental space-time symmetry framework that can encompass all of physics, including gravity, for all inertial and non-inertial frames of reference.

Product Details

ISBN-13:	9789814436182
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	09/18/2013
Series:	Advanced Series On Theoretical Physical Science , #11
Pages:	288
Product dimensions:	6.10(w) x 9.00(h) x 0.90(d)

Table of Contents

Preface vii

Overview xvii

About the Author xxxi

Part I The Taiji Symmetry Framework Leonardo Hsu Jong-Ping Hsu 1

1 Space-Time Symmetry, Natural Units and Fundamental Constants 3

1-1 Underpinnings 3

1-2 Physical basis for the system of natural units 4

1-3 Nature of the fundamental constants 8

References 10

2 The Taiji Relativity Framework 13

2-1 A new space-time framework 13

2-2 Taiji relativity 14

2-3 Operationalization of taiji time 16

2-4 Conceptual difference between taiji relativity and Special Relativity 17

2-5 A short digression: The role of a second postulate 18

References 20

3 The Principle of Limiting Continuation of Physical Laws and Coordinate Transformations for Frames with Constant Accelerations 23

3-1 The principle of limiting continuation 23

3-2 Constant linear acceleration: The Wu transformations 25

3-3 Operational meaning of the space-time coordinates and 'constant-linear-acceleration' 28

3-4 Singular walls and horizons in accelerated frames 30

3-5 The Wu pseudo-group 32

3-6 Relationship between the Wu and Møller transformations 35

3-7 Experimental tests of the Wu transformations 38

References 43

4 Coordinate Transformations for Frames with Arbitrary Linear Accelerations and the Taiji Pseudo-Group 45

4-1 Arbitrary Linear Accelerations: The Taiji Transformations 45

4-2 Poincaré Metric Tensors for Arbitrary-Linear-Acceleration Frames 49

4-3 New Properties of the Taiji Transformations 50

4-4 Physical Implications 54

4-5 Experimental Tests of the Taiji Transformations 58

References 59

5 Coordinate Transformations for Rotating Frames and Experimental Tests 61

5-1 Rotational taiji transformations 61

5-2 Metric tensors for the space-time of rotating frames 66

5-3 The rotational pseudo-group 67

5-4 Physical implications 69

5-5 Experimental tests of the rotational taiji transformations 72

References 78

6 Conservation Laws and Symmetric Energy-Momentum Tensors 79

6-1 Conservation laws in the Taiji symmetry framework 79

6-2 Symmetric energy-momentum tensors and variations of metric tensors in taiji space-time 80

6-3 Integral forms of conservation laws in non-inertial frames 83

6-4 Symmetry implicatiohs of global and local space-time translations 87

References 89

Part II Quantum Yang-Mills Gravity Jong-Ping Hsu Leonardo Hsu 91

7 The Yang-Mills-Utiyama-Weyl Framework for Internal and External Gauge Symmetries 93

7-1 The Yang-Mills-Utiyama-Weyl framework 93

7-2 The Levi-Civita connection and interpretations of Einstein gravity 95

7-3 Weyl's parallel transport of scale and electromagnetic fields 97

7-4 Curvatures on the connections 99

7-5 Taiji symmetry and the space-time translational symmetry group T₄ 102

References 106

8 Yang-Mills Gravity Based on Flat Space-time and Effective Curved Space-Time for Motions of Classical Objects 109

8-1 Translational gauge transformations in taiji space-time 109

8-2 Translational gauge symmetry and the field-theoretic origin of effective metric tensors 112

8-3 Gauge invariant action and quadratic gauge curvature 113

8-4 The gravitational field equation and fermion equations in general frames of reference 115

8-5 Derivations of the T₄ eikonal and Einstein-Grossmann equations in the geometric-optics limit 118

8-6 Effective action for classical objects and Gauge Invariance 120

8-7 Classical objects as a coherent collection of constituent particles 122

8-8 Remarks on Yang-Mills gravity and teleparallel gravity 123

References 126

9 Experimental Tests of Classical Yang-Mills Gravity 129

9-1 Motion in a central gravitational field 129

9-2 The perihelion shift of Mercury 133

9-3 Deflection of light in a gravitational field 135

9-4 Gravitational quadrupole radiation 137

References 141

10 The S-Matrix in Yang-Mills Gravity 143

10-1 The gauge-invariant action and gauge conditions 143

10-2 Feynman-DeWitt-Mandelstam (FDM) ghost fields in Yang-Mills gravity 144

10-3 Unitarity and gauge invariance of the S-matrix and FDM ghost particles 147

10-4 Discussion 148

References 150

11 Quantization of Yang-Mills Gravity and Feynman-Dyson Rules 153

11-1 A gauge invariant action for gravitons and fermions and their field equations 153

11-2 The Feynman-Dyson rules for quantum Yang-Mills gravity 157

References 161

12 Gravitational Self-Energy of the Graviton 163

12-1 Graviton self-energy in the DeWitt gauge 163

12-2 Graviton self-energy in a general gauge 166

12-3 Discussion 169

References 170

13 Space-Time Gauge Identities and Finite-Loop Renormalization 173

13-1 Space-time (T₄) gauge identities 173

13-2 Space-time gauge identities and a general graviton propagator 176

13-3 Gauge identities in quantum electrodynamics with a non-linear gauge condition 178

13-4 The infinite continuous group of general coordinate transformations in flat space-time 180

13-5 Remarks on ultraviolet divergences and finite-loop renormalization for gravity 184

References 187

14 A Unified Gravity-Electroweak Model 191

14-1 The gauge covariant derivative and gauge curvatures of a unified gravity-electroweak model 191

14-2 The Lagrangian in the gravielecweak model 194

14-3 The equations of motion for quantum and classical particles 194

14-4 Violations of U₁ and SU₂ gauge symmetries by gravity 198

References 200

15 A Unified Gravity-Strong Force Model 201

15-1 Unified gauge covariant derivatives and gauge curvatures 201

15-2 The action of the unified model and violations of local SU₃ gauge symmetry by gravity 202

15-3 Effective curved space-time for motions of quarks and gluons in the classical limit 205

15-4 Discussion 207

References 208

16 Outlook 211

16-1 Taiji space-time - a basic framework for all physics 211

16-2 The cosmic Lee-Yang force and a linear potential for the accelerated expansion of the universe 212

16-3 Possible origins of mass in a unified model: constant vacuum field or Higgs field? 215

16-4 Finite quantum gravity and a possible departure from exact Lorentz invariance at high energies 217

16-5 Toward a total unification of all interactions 220

16-6 Conclusion 223

References 223

Appendix A The Fock-Hilbert Approach to Local Symmetry and Conservation Laws in General Frames of Reference 227

A-1 Conserved Charges in Inertial and Non-inertial Frames 227

A-2 Energy-Momentum Tensor of Fermions 230

References 231

Appendix B Calculations of H^μv in the Gravitational Field Equation 233

B-1 Evaluations of the component H⁰⁰ 233

B-2 Evaluations of the component H¹¹ 236

B-3 Evaluations of the component H²² 237

Appendix C Tensor Properties of Physical Quantities in Taiji Space-Time 241

Author Index 245

Subject Index 249