Overview

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.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 Yang-Mills 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 Yang–Mills' profound thoughts present a great challenge to physicists and mathematicians in the 21st century.Contents: The Dawn of Gravitation: The Mathematical Principles of Natural Philosophy (I Newton) On the Dynamics of the Electron (H Poincaré) Einstein's Deepest Insight and Its Early Impacts: Outline of a Generalized Theory of Relativity and of a Theory of Gravitation (A Einstein & M Grossmann) The Foundation of the General Theory of Relativity (A Einstein) On a Generalization of the Concept of Riemann Curvature and Spaces with Torsion (E Cartan) The Scalar-Tensor Theory of Gravity: Formation of the Stars and Development of the Universe (P Jordan) Yang–Mills' Deepest Insight and Its Relation to Gravity: Conservation of Isotopic Spin and Isotopic Gauge Invariance (C N Yang & R L Mills) Conservation of Heavy Particles and Generalized Gauge Transformations (T D Lee & C N Yang) Invariant Theoretical Interpretation of Interaction (R Utiyama) Accelerated Frames: Generalizing the Lorentz Transformations: On Homogeneous Gravitational Fields in the General Theory of Relativity and the Clock Paradox (C Møller) The Clock Paradox in the Relativity Theory (T Y Wu & Y C Lee) Four-dimensional Symmetry of Taiji Relativity and Coordinate Transformations Based on a Weaker Postulate for the Speed of Light (J P Hsu & L Hsu) Quantum Gravity and 'Ghosts' Quantum Theory of Gravitation (R P Feynman) Quantum Theory of Gravity, III Applications of the Covariant Theory (B S DeWitt) Feynman Diagrams for the Yang–Mills Field (L D Faddeev & V N Popov) Missed Opportunities (F J Dyson) Gauge Theories of Gravity: Extended Translation Invariance and Associated Gauge Fields (K Hayashi & T Nakano) Gravitational Field as a Generalized Gauge Field (R Utiyama & T Fukuyama) Alternate Approaches to Gravity: Roads Less Traveled By: Fixation of Coordinates in the Hamiltonian Theory of Gravitation (P A M Dirac) New General Relativity (K Hayashi & T Shirafuji) Relativistic Theory of Gravitation (A A Logunov & M A Mestvirishvili) Yang–Mills Gravity: A Union of Einstein-Grossmann Metric with Yang–Mills Tensor Fields in Flat Spacetime with Translation Symmetry (J P Hsu)

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