100 Years of Gravity and Accelerated Frames: The Deepest Insights of Einstein and Yang-Mills

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World Scientific, 2005 - Einstein field equations - 623 pages
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This collection of papers presents ideas and problems arising over the past 100 years regarding classical and quantum gravity, gauge theories of gravity, and spacetime transformations of accelerated frames. Both Einstein''s theory of gravity and the YangOCoMills theory are gauge invariant. The invariance principles in physics have transcended both kinetic and dynamic properties and are at the very heart of our understanding of the physical world. In this spirit, this book attempts to survey the development of various formulations for gravitational and YangOCoMills fields and spacetime transformations of accelerated frames, and to reveal their associated problems and limitations. The aim is to present some of the leading ideas and problems discussed by physicists and mathematicians. We highlight three aspects: formulations of gravity as a YangOCoMills field, first discussed by Utiyama; problems of gravitational theory, discussed by Feynman, Dyson and others; spacetime properties and the physics of fields and particles in accelerated frames of reference. These unfulfilled aspects of Einstein and YangOCoMills'' profound thoughts present a great challenge to physicists and mathematicians in the 21st century."
 

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Contents

A The Mathematical Principles of Natural Philosophy Extract
2
B On the Dynamics of the Electron Extract
13
On the Relativity Principle and the Conclusions Drawn from It Extract
33
A Outline of a Generalized Theory of Relativity and of a Theory
48
B The Foundation of the General Theory of Relativity
65
The Foundation of Physics
120
On a Generalization of the Concept of Riemann Curvature
132
B On the Physical Interpretation of P Jordans Extended Theory of Gravitation Extract
140
F S Matrix for YangMills and Gravitational Fields Extract
339
G Missed Opportunities Extract with a brief comment of the author
347
Gauge Theories of Gravity
354
B Gravitational Field as a Generalized Gauge Field
371
Integral Formalism for Gauge Fields with a brief comment
387
E Einstein Lagrangian as the Translational YangMills Lagrangian
393
Roads Less Traveled
401
B New General Relativity with Addendun
409

YangMills Deepest Insight and Its Relation to Gravity
149
B Conservation of Heavy Particles and Generalized Gauge Transformations
155
Lorentz Invariance and the Gravitational Field
168
Generalizing the Lorentz Transformations
179
B Physical Consequences of a Coordinate Transformation to
204
The Clock Paradox in the Relativity Theory
223
Fourdimensional Symmetry of Taiji Relativity and Coordinate Transformations
240
E Generalized Lorentz Transformations for Linearly Accelerated Frames with
247
F Generalizing Lorentz Transformations for Accelerated Frames
258
Quantum Gravity and Ghosts
271
B Quantum Theory of Gravity II The Manifestly Covariant Theory Extract
298
Quantum Theory of Gravity III Applications of the Covariant Theory
307
Feynman Diagrams for the YangMills Field
325
Relativistic Theory of Gravitation
442
A Union of EinsteinGrossmann Metric with YangMills
462
A Empirical Foundations of the Relativistic Gravity
476
B Binary Pulsars and Relativistic Gravity
494
Other Perspectives
503
B Gauge Fields
512
Magnetic Monopoles Fiber Bundles and Gauge Fields
527
Historical Origins and Some Modern Developments
539
E String Theory as a Generalization of Gauge Symmetry
562
F The Cosmological Constant Problem
569
G The Cosmological Constant and Dark Energy Extract
592
A Marcel Grossmann 18781936
620
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