Knot theory and quantum gravity

Journal Article · Mon Sep 05 00:00:00 EDT 1988 · Phys. Rev. Lett.; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.61.1155· OSTI ID:6852074

Rovelli, C; Smolin, L

A new represenatation 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 diffeomorphisms constraint 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.

• Research Organization: Sezione di Roma, INFN, University of Rome, Rome, Italy
• OSTI ID: 6852074
• Journal Information: Phys. Rev. Lett.; (United States), Journal Name: Phys. Rev. Lett.; (United States) Vol. 61:10; ISSN PRLTA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
CANONICAL TRANSFORMATIONS
FIELD THEORIES
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
INVARIANCE PRINCIPLES
LIMITING VALUES
MATHEMATICAL OPERATORS
MATHEMATICS
METRICS
PERTURBATION THEORY
QUANTIZATION
QUANTUM FIELD THEORY
QUANTUM GRAVITY
QUANTUM OPERATORS
TOPOLOGY
TRANSFORMATIONS