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

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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 Yang-Mills 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 Yang-Mills fields and spacetime transformations of accelerated frames, and to reveal their associated problems and limitations.
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Table of Contents

Remarks on the development of the gravitational and Yang-Mills fields, and accelerated frames
The mathematical principles of natural philosophy (extract) : rules of reasoning in philosophy phenomena, or appearances 2
On the dynamics of the electron (extract) : introduction, hypotheses concerning gravitation 13
On the relativity principle and the conclusions drawn from it (extract) 33
Outline of a generalized theory of relativity and of a theory of gravitation (extract) 48
The foundation of the general theory of relativity 65
The foundation of physics 120
On a generalization of the concept of Riemann curvature and spaces with torsion 132
Formation of the stars and development of the universe 136
On the physical interpretation of P. Jordan's extended theory of gravitation (extract) 140
Mach's principle and a relativistic theory of gravitation (extract) 142
Conservation of isotopic spin and isotopic gauge invariance 150
Conservation of heavy particles and generalized gauge transformations 155
Invariant theoretical interpretation of interaction 157
Lorentz invariance and the gravitational field 168
On homogeneous gravitational fields in the general theory of relativity and the clock paradox 180
Physical consequences of a co-ordinate transformation to a uniformly accelerating frame 204
The clock paradox in the relativity theory 223
Four-dimensional symmetry of Taiji relativity and coordinate transformations based on a weaker postulate for the speed of light (extract) 240
Generalized Lorentz transformations for linearly accelerated frames with limiting four-dimensional symmetry 247
Generalizing Lorentz transformations for accelerated frames and their physical implications 258
Quantum theory of gravitation 272
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 Yang-Mills field 325
Feynman rules for electromagnetic and Yang-Mills fields from the gauge-independent field-theoretic formalism (extract) 327
S matrix for Yang-Mills and gravitational fields (extract) 339
Missed opportunities (extract, with a brief comment of the author) introduction, general coordinate invariance 347
Extended translation invariance and associated gauge fields 354
Gravitational field as a generalized gauge field 371
Integral formalism for gauge fields (with a brief comment) 387
Yang's gravitational field equations 391
Einstein Lagrangian as the translational Yang-Mills Lagrangian 393
De Sitter and Poincare gauge-invariant fermion Lagrangians and gravity 398
Fixation of coordinates in the Hamiltonian theory of gravitation 402
New general relativity (with addendun) 409
Relativistic theory of gravitation 442
Yang-Mills gravity : a union of Einstein-Grossmann metric with Yang-Mills tensor fields in flat spacetime with translation symmetry 462
Empirical foundations of the relativistic gravity 476
Binary pulsars and relativistic gravity 494
Concept of nonintegrable phase factors and global formulation of gauge fields (extract) 504
Gauge fields 512
Magnetic monopoles, fiber bundles, and gauge fields 527
Gauge theory : historical origins and some modern developments 539
String theory as a generalization of gauge symmetry 562
The cosmological constant problem 569
The cosmological constant and dark energy (extract) 592
App. A Marcel Grossmann (1878-1936) 618
App. B Remembering Robert L. Mills 622
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