### 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 language | English |
---|---|

Pages (from-to) | 1867-1874 |

Number of pages | 8 |

Journal | Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences |

Volume | 366 |

Issue number | 1871 |

DOIs | |

Publication status | Published - 28 May 2008 |

### Keywords

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

### Cite this

**Gauge formulation of general relativity using conformal and spin symmetries.** / Wang, Charles H. -T.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Gauge formulation of general relativity using conformal and spin symmetries

AU - Wang, Charles H. -T.

PY - 2008/5/28

Y1 - 2008/5/28

N2 - 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.

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.

KW - general relativity

KW - quantum gravity

KW - conformal geometry

KW - quantum-gravity

KW - dynamics

U2 - 10.1098/rsta.2007.2193

DO - 10.1098/rsta.2007.2193

M3 - Article

VL - 366

SP - 1867

EP - 1874

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences

SN - 1364-503X

IS - 1871

ER -