General Relativity and the Theory of a Self-Interacting Abelian Gauge Field

Daniel Wisnivesky

doi:10.4236/jmp.2017.88076

Abstract

The standard theory of general relativity (GR) can be written in a form proposed by Eddington using the parametric representation of the metric tensor. In this paper, the equations of the standard theory of GR using the parametric representation are first developed. Afterwards, the fundamental ideas of a new type of abelian self-interacting gauge theory are presented. Finally, it is shown that the gauge field equations of this new theory are identical to the parametric form of Einstein’s equations of general relativity. It is concluded that classical gravity can be described either by the usual theory of GR in a curved space-time or, alternatively as a self-interacting gauge theory independent of the dynamics of space-time.

Highlights

IntroductionThree of the fundamental forces in nature are described by Yang and Mills quantum field gauge theories on flat space-time, the fourth interaction, gravity, being a classical theory involving the dynamics of curved space-time is the exception
Three of the fundamental forces in nature are described by Yang and Mills quantum field gauge theories on flat space-time, the fourth interaction, gravity, being a classical theory involving the dynamics of curved space-time is the exception.The original theory of general relativity (GR) in terms of the metric tensor of curved space-time has been the subject of alternative formulations by different authors during the last 100 years
The standard theory of general relativity (GR) can be written in a form proposed by Eddington using the parametric representation of the metric tensor

Summary

Introduction

Three of the fundamental forces in nature are described by Yang and Mills quantum field gauge theories on flat space-time, the fourth interaction, gravity, being a classical theory involving the dynamics of curved space-time is the exception. The original theory of general relativity (GR) in terms of the metric tensor of curved space-time has been the subject of alternative formulations by different authors during the last 100 years. Eddington [9], introduced the idea of representing the metric tensor of a four dimensional curved space-time in terms of ten parameters. In the book “The Mathematical Theory of Relativity” [9], Eddington mentions the possibility of representing the metric tensor of a four-dimensional curved space-time in terms of ten parameters. With this in mind, the equations of the standard theory of GR using the parametric representation of the metric tensor will be developed. The rectangular matrix φαa is defined in terms of the inverse metric g ab and ∂bξ β as: φ=αa g ab∂bξ βηαβ (4)

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The Self-Interacting Abelian Gauge Theory

Conclusion