Space-Time Symmetry and Quantum Yang–Mills Gravity

The following sections are included:

• Preface

• Contents

• Overview

• About the Author

The following sections are included:

• Underpinnings

• Physical basis for the system of natural units
  • Equivalence of length and time
  • Equivalence of mass and length
  • Equivalence of current and length
  • Equivalence of temperature and length

• Nature of the fundamental constants

• References

The following sections are included:

• A new space-time framework

• Taiji relativity

• Operationalization of taiji time

• Conceptual difference between taiji relativity and special relativity

• A short digression: The role of a second postulate

• References

The following sections are included:

• The principle of limiting continuation

• Constant linear acceleration: The Wu transformations

• Operational meaning of the space-time coordinates and ‘constant-linear-acceleration’

• Singular walls and horizons in accelerated frames

• The Wu pseudo-group

• Relationship between the Wu and Møller transformations

• Experimental tests of the Wu transformations

• References

The following sections are included:

• Arbitrary linear accelerations: The Taiji transformations

• Poincaré metric tensors for arbitrary-linear-acceleration frames

• New properties of the Taiji transformations

• Physical implications
  • Physical implications
  • Space-time-dependent speed of light in ALA frames
  • Operational definition of the space-time coordinates in ALA frames
  • The velocity-addition laws in ALA frames
  • Classical electrodynamics in inertial and non-inertial frames
  • Generalized Klein–Gordon and Dirac equations for non-inertial frames

• Experimental tests of the Taiji transformations

• References

The following sections are included:

• Rotational taiji transformations

• Metric tensors for the space-time of rotating frames

• The rotational pseudo-group

• Physical implications
  • The invariant action for electrodynamics in rotating frames
  • Absolute contraction of a rotating radius and absolute slow-down of a rotating clock
  • The covariant four-momentum in a rotating frame

• Experimental tests of the rotational taiji transformations
  • Absolute dilation of decay length for particle decay in circular motion
  • Davies–Jennison experiment
  • Thim–s experiment with orbiting receivers

• References

The following sections are included:

• Conservation laws in the Taiji symmetry framework

• Symmetric energy–momentum tensors and variations of metric tensors in taiji space-time

• Integral forms of conservation laws in non-inertial frames

• Symmetry implications of global and local space-time translations

• References

The following sections are included:

• The Yang–Mills–Utiyama–Weyl framework

• The Levi-Civita connection and interpretations of Einstein gravity

• Weyl's parallel transport of scale and electromagnetic fields

• Curvatures on the connections

• Taiji symmetry and the space-time translational symmetry group T₄
  • Taiji space-time symmetry
  • T₄ gauge transformations and groups
  • T₄ and Weyl’s parallel transports of ‘scale’ s(t ) and T₄ gauge curvature

• References

The following sections are included:

• Translational gauge transformations in taiji space-time

• Translational gauge symmetry and the field-theoretic origin of effective metric tensors

• Gauge invariant action and quadratic gauge curvature

• The gravitational field equation and fermion equations in general frames of reference

• Derivations of the T₄ eikonal and Einstein–Grossmann equations in the geometric-optics limit

• Effective action for classical objects and gauge invariance

• Classical objects as a coherent collection of constituent particles

• Remarks on Yang–Mills gravity and teleparallel gravity
  • Gauge covariant derivative
  • Gauge curvature
  • Gravitational action

• References

The following sections are included:

• Motion in a central gravitational field

• The perihelion shift of Mercury

• Deflection of light in a gravitational field

• Gravitational quadrupole radiation

• References

The following sections are included:

• The gauge-invariant action and gauge conditions

• Feynman–DeWitt–Mandelstam (FDM) ghost fields in Yang–Mills gravity

• Unitarity and gauge invariance of the S-matrix and FDM ghost particles

• Discussion

• References

The following sections are included:

• A gauge invariant action for gravitons and fermions and their field equations

• The Feynman–Dyson rules for quantum Yang–Mills gravity

• References

The following sections are included:

• Graviton self-energy in the DeWitt gauge

• Graviton self-energy in a general gauge

• Discussion

• References

The following sections are included:

• Space-time (T₄) gauge identities

• Space-time gauge identities and a general graviton propagator

• Gauge identities in quantum electrodynamics with a non-linear gauge condition

• The infinite continuous group of general coordinate transformations in flat space-time

• Remarks on ultraviolet divergences and finite-loop renormalization for gravity

• References

The following sections are included:

• The gauge covariant derivative and gauge curvatures of a unified gravity–electroweak model

• The Lagrangian in the gravielecweak model

• The equations of motion for quantum and classical particles
  • The classical equation of motion for gauge bosons
  • The classical equations of motion for gravitons
  • The classical equations of motion for leptons, quarks and Higgs particles

• Violations of U₁ and SU₂ gauge symmetries by gravity

• References

The following sections are included:

• Unified gauge covariant derivatives and gauge curvatures

• The action of the unified model and violations of local SU₃ gauge symmetry by gravity

• Effective curved space-time for motions of quarks and gluons in the classical limit

• Discussion

• References

The following sections are included:

• Taiji space-time—a basic framework for all physics

• The cosmic Lee–Yang force and a linear potential for the accelerated expansion of the universe

• Possible origins of mass in a unified model: constant vacuum field or Higgs field?

• Finite quantum gravity and a possible departure from exact Lorentz invariance at high energies

• Toward a total unification of all interactions

• Conclusion

• References

The following sections are included:

• Appendix A. The Fock–Hilbert Approach to Local Symmetry and Conservation Laws in General Frames of Reference
  • Conserved Charges in Inertial and Non-inertial Frames
  • Energy-Momentum Tensor of Fermions

• References

• Appendix B. Calculations of H^μν in the Gravitational Field Equation
  • Evaluations of the component H⁰⁰
  • Evaluations of the component H¹¹
  • Evaluations of the component H²²

• Appendix C. Tensor Properties of Physical Quantities in Taiji Space-Time

• Author Index

• Subject Index