## 100 Years of Gravity and Accelerated Frames: The Deepest Insights of Einstein and Yang-MillsThis 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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### Common terms and phrases

accelerated frames amplitude arbitrary C. N. Yang calculation CLA frame classical clock components condition conservation law coordinate transformation corresponding cosmological constant covariant derivative curvature defined diagrams differential Dirac discussed Einstein electrodynamics electromagnetic field energy-momentum tensor equations of motion equivalent expression Feynman field equations field theory formalism four-dimensional gauge fields gauge invariance gauge theory gauge transformation geometry gravitational field graviton Green's functions identity inertial frame integral interaction isotopic spin Lagrangian density Lett linear Lorentz transformation mass mathematical matrix matter measured metric tensor Minkowski momentum observed obtain parallel vector fields parameters particle Pauli photon Phys physical Poincare potential principle problem propagator pulsar quantities relation relativistic respect result Riemannian satisfy solution space space-time spinor string theory symmetry theorem theory of gravitation theory of relativity tion translation universe vacuum vanish variables velocity wave function Weyl Yang-Mills field zero