Knot Theory and Quantum Gravity

Carlo Rovelli and Lee Smolin
Phys. Rev. Lett. 61, 1155 – Published 5 September 1988
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Abstract

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.

  • Received 13 June 1988

DOI:https://doi.org/10.1103/PhysRevLett.61.1155

©1988 American Physical Society

Authors & Affiliations

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

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

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Vol. 61, Iss. 10 — 5 September 1988

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