Gauge formulation of general relativity using conformal and spin symmetries

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Abstract

The gauge symmetry inherent in Maxwell's electromagnetics has a profound impact on modern physics. Following the successful quantization of electromagnetics and other higher order gauge. eld theories, the gauge principle has been applied in various forms to quantize gravity. A notable development in this direction is loop quantum gravity based on the spin-gauge treatment. This paper considers a further incorporation of the conformal gauge symmetry in canonical general relativity. This is a new conformal decomposition in that it is applied to simplify recently formulated parameter-free construction of spin-gauge variables for gravity. The resulting framework preserves many main features of the existing canonical framework for loop quantum gravity regarding the spin network representation and Thiemann's regularization. However, the Barbero Immirzi parameter is converted into the conformal factor as a canonical variable. It behaves like a scalar. eld but is somehow non-dynamical since the Hamiltonian constraint does not depend on its momentum. The essential steps of the mathematical derivation of this parameter-free framework for the spin-gauge variables of gravity are spelled out. The implications for the loop quantum gravity programme are briefly discussed.

Original languageEnglish
Pages (from-to)1867-1874
Number of pages8
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences
Volume366
Issue number1871
DOIs
Publication statusPublished - 28 May 2008

Keywords

  • general relativity
  • quantum gravity
  • conformal geometry
  • quantum-gravity
  • dynamics

Cite this

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title = "Gauge formulation of general relativity using conformal and spin symmetries",
abstract = "The gauge symmetry inherent in Maxwell's electromagnetics has a profound impact on modern physics. Following the successful quantization of electromagnetics and other higher order gauge. eld theories, the gauge principle has been applied in various forms to quantize gravity. A notable development in this direction is loop quantum gravity based on the spin-gauge treatment. This paper considers a further incorporation of the conformal gauge symmetry in canonical general relativity. This is a new conformal decomposition in that it is applied to simplify recently formulated parameter-free construction of spin-gauge variables for gravity. The resulting framework preserves many main features of the existing canonical framework for loop quantum gravity regarding the spin network representation and Thiemann's regularization. However, the Barbero Immirzi parameter is converted into the conformal factor as a canonical variable. It behaves like a scalar. eld but is somehow non-dynamical since the Hamiltonian constraint does not depend on its momentum. The essential steps of the mathematical derivation of this parameter-free framework for the spin-gauge variables of gravity are spelled out. The implications for the loop quantum gravity programme are briefly discussed.",
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AB - The gauge symmetry inherent in Maxwell's electromagnetics has a profound impact on modern physics. Following the successful quantization of electromagnetics and other higher order gauge. eld theories, the gauge principle has been applied in various forms to quantize gravity. A notable development in this direction is loop quantum gravity based on the spin-gauge treatment. This paper considers a further incorporation of the conformal gauge symmetry in canonical general relativity. This is a new conformal decomposition in that it is applied to simplify recently formulated parameter-free construction of spin-gauge variables for gravity. The resulting framework preserves many main features of the existing canonical framework for loop quantum gravity regarding the spin network representation and Thiemann's regularization. However, the Barbero Immirzi parameter is converted into the conformal factor as a canonical variable. It behaves like a scalar. eld but is somehow non-dynamical since the Hamiltonian constraint does not depend on its momentum. The essential steps of the mathematical derivation of this parameter-free framework for the spin-gauge variables of gravity are spelled out. The implications for the loop quantum gravity programme are briefly discussed.

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