Knots and Quantum Gravity: Progress and Prospects

Details Knots and Quantum Gravity: Progress and Prospects Knots and Quantum Gravity: Progress and Prospects

1994-10-13

arxiv.org/abs/gr-qc/9410018v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages in LaTeX

Scientific paper

Recent work on the loop representation of quantum gravity has revealed previously unsuspected connections between knot theory and quantum gravity, or more generally, 3-dimensional topology and 4-dimensional generally covariant physics. We review how some of these relationships arise from a `ladder of field theories' including quantum gravity and BF theory in 4 dimensions, Chern-Simons theory in 3 dimensions, and the G/G gauged WZW model in 2 dimensions. We also describe the relation between link (or multiloop) invariants and generalized measures on the space of connections. In addition, we pose some research problems and describe some new results, including a proof (due to Sawin) that the Chern-Simons path integral is not given by a generalized measure.

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