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APS » Journals » Phys. Rev. Lett. » Volume 61 » Issue 10
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Phys. Rev. Lett. 61, 1155–1158 (1988)

Knot Theory and Quantum Gravity

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Carlo Rovelli
Sezione di Roma, Instituto Nazionale di Fisica Nucleare, University of Rome, Rome, Italy

Lee Smolin*
Department of Physics, Yale University, New Haven, Connecticut 06520

Received 13 June 1988; published in the issue dated 5 September 1988

A new representation for quantum general relativity is described, which is defined in terms of functionals of sets of loops in three-space. In this representation exact solutions of the quantum constraints may be obtained. This result is related to the simplification of the constraints in Ashtekar's new formalism. We give in closed form the general solution of the diffeomorphism constraints and a large class of solutions of the full set of constraints. These are classified by the knot and link classes of the spatial three-manifold.

© 1988 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.61.1155
DOI:
10.1103/PhysRevLett.61.1155
PACS:
04.60.+n, 02.40.+m

*Present address: Department of Physics, Syracuse University, Syracuse, NY 13210.

 
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