### Abstract

The emergence of loop quantum gravity over the past two decades has stimulated a great resurgence of interest in unifying general relativity and quantum mechanics. Among a number of appealing features of this approach is the intuitive picture of quantum geometry using spin networks and powerful mathematical tools from gauge field theory. However, the present form of loop quantum gravity suffers from a quantum ambiguity, owing to the presence of a free ( Barbero Immirzi) parameter. Following the recent progress on conformal decomposition of gravitational fields, we present a new phase space for general relativity. In addition to spin-gauge symmetry, the new phase space also incorporates conformal symmetry making the description parameter free. The Barbero - Immirzi ambiguity is shown to occur only if the conformal symmetry is gauge fixed prior to quantization. By withholding its full symmetries, the new phase space offers a promising platform for the future development of loop quantum gravity. This paper aims to provide an exposition, at a reduced technical level, of the above theoretical advances and their background developments. Further details are referred to cited references.

Original language | English |
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Pages (from-to) | 3375-3388 |

Number of pages | 14 |

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

Volume | 364 |

DOIs | |

Publication status | Published - 2006 |

### Keywords

- general relativity
- loop quantum gravity
- conformal geometry
- canonical quantization
- Immirzi parameter
- formulation
- variables
- dynmics
- real