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

Steffen Gielen

Symmetry, integrability and geometry: methods and applications, Tome 7 (2011)

Résumé

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.

Détail

Keywords: canonical quantum gravity, semisimple Lie algebras, infinite-dimensional manifolds.
Mots-clés : gravitational connection

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