关于重力的规范形式论的注解

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Theoretical and Mathematical Physics Pub Date : 2022-12-16 DOI:10.4310/atmp.2023.v27.n1.a6
E. Witten
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引用次数: 11

摘要

我们描述了一个简单的量规固定,它导致在渐近反德西特时空中构造量子引力的量子希尔伯特空间,对所有阶的微扰理论都有效。该构造是由引力在渐近反德西特时空中的相空间与共切束的关系所驱动的。我们描述了关于这种关系的已知内容,以及一些可能是真实的扩展。一个关键的事实是,在某些条件下,爱因斯坦哈密顿约束方程可以被看作是一种测量固定柯西超曲面度规的共形重标度群的方法。我们在反德西特引力中所遵循的类似程序可以得到克莱因-戈登粒子的标准结果。
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A note on the canonical formalism for gravity
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.
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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