Spin Networks in Nonperturbative Quantum Gravity

Details Spin Networks in Nonperturbative Quantum Gravity Spin Networks in Nonperturbative Quantum Gravity

1995-04-21

arxiv.org/abs/gr-qc/9504036v2

in The Interface of Knots and Physics, ed. Louis Kauffman, A.M.S., Providence, 1996, pp. 167-203

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

41 pages in LaTeX

Scientific paper

A spin network is a generalization of a knot or link: a graph embedded in space, with edges labelled by representations of a Lie group, and vertices labelled by intertwining operators. Such objects play an important role in 3-dimensional topological quantum field theory, functional integration on the space A/G of connections modulo gauge transformations, and the loop representation of quantum gravity. Here, after an introduction to the basic ideas of nonperturbative canonical quantum gravity, we review a rigorous approach to functional integration on A/G in which L^2(A/G) is spanned by states labelled by spin networks. Then we explain the `new variables' for general relativity in 4-dimensional spacetime and describe how canonical quantization of gravity in this formalism leads to interesting applications of these spin network states.

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