The Space of Connections as the Arena for (Quantum) Gravity

Symmetry Integrability and Geometry-Methods and Applications

article

Steffen Gielen¹ 

[1] Albert Einstein Institute

关键词: canonical quantum gravity;    gravitational connection;    semisimple Lie algebras;    infinite-dimensional manifolds;   

DOI  :  10.3842/SIGMA.2011.104

来源: National Academy of Science of Ukraine

【 摘 要 】

We review some properties of the space of connections as the natural arena for canonical (quantum) gravity, and compare to the case of the superspace of 3-metrics. We detail how a 1-parameter family of metrics on the space of connections arises from the canonical analysis for general relativity which has a natural interpretation in terms of invariant tensors on the algebra of the gauge group. We also review the description of canonical GR as a geodesic principle on the space of connections, and comment on the existence of a time variable which could be used in the interpretation of the quantum theory.

【 授权许可】

Unknown