## Abstract

We describe a simple gauge-fixing that leads to a construction of a quantum Hilbert space for quantum gravity in an asymptotically Anti de Sitter spacetime, valid to all orders of perturbation theory. The construction is motivated by a relationship of the phase space of gravity in asymptotically Anti de Sitter spacetime to a cotangent bundle. We describe what is known about this relationship and some extensions that might plausibly be true. A key fact is that, under certain conditions, the Einstein Hamiltonian constraint equation can be viewed as a way to gauge fix the group of conformal rescalings of the metric of a Cauchy hypersurface. An analog of the procedure that we follow for Anti de Sitter gravity leads to standard results for a Klein-Gordon particle.

Original language | English (US) |
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Pages (from-to) | 311-380 |

Number of pages | 70 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 27 |

Issue number | 1 |

DOIs | |

State | Published - 2023 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Physics and Astronomy(all)