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

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Gielen,  Steffen
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1111.2672
(Preprint), 212KB

sigma11-104.pdf
(Any fulltext), 369KB

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Citation

Gielen, S. (2011). The Space of Connections as the Arena for (Quantum) Gravity. SIGMA: Special Issue on Loop Quantum Gravity and Cosmology, 7, 104-116. doi:10.3842/SIGMA.2011.104.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-3131-5
Abstract
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.