Space-Time Symmetry and Quantum YangMills Gravity

How Space-Time Translational Gauge Symmetry Enables the Unification of Gravity with Other Forces

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.

Contents:

• The Taiji Symmetry Framework (Leonardo Hsu and Jong-Ping Hsu):

  • Space-Time Symmetry, Natural Units and Fundamental Constants
  • The Taiji Relativity Framework
  • The Principle of Limiting Continuation of Physical Laws and Coordinate Transformations for Frames with Constant Accelerations
  • Coordinate Transformations for Frames with Arbitrary Linear Accelerations and the Taiji Pseudo-Group
  • Coordinate Transformations for Rotating Frames and Experimental Tests
  • Conservation Laws and Symmetric Energy–Momentum Tensors

• Quantum Yang–Mills Gravity (Jong-Ping Hsu and Leonardo Hsu):

  • The Yang–Mills–Utiyama–Weyl Framework for Internal and External Gauge Symmetries
  • Yang–Mills Gravity Based on Flat Space-Time and Effective Curved Space-Time for Motions of Classical Objects
  • Experimental Tests of Classical Yang–Mills Gravity
  • The S-Matrix in Yang–Mills Gravity
  • Quantization of Yang–Mills Gravity and Feynman–Dyson Rules
  • Gravitational Self-Energy of the Graviton
  • Space-Time Gauge Identities and Finite-Loop Renormalization
  • A Unified Gravity–Electroweak Model
  • A Unified Gravity–Strong Force Model
  • Outlook

• Appendices:

  • The Fock–Hilbert Approach to Local Symmetry and Conservation Laws in General Frames of Reference
  • Calculations of Hμν in the Gravitational Field Equation
  • Tensor Properties of Physical Quantities in Taiji Space-Time

Readership: Graduate students and researchers in quantum gravity.
Key Features:

• Quantum Yang–Mills gravity differs from all previous formulations of gravity in its simplicity of the Lagrangian and in its physical coherence
• The book contains a unique treatment of the ‘taiji symmetry’ framework
• The book discusses a total unified model for all known interactions based on a generalized Yang–Mills framework