Knot theory and the dynamics of quantum general relativity

DOI10.1088/0264-9381/13/11/001zbMATH Open0864.57007arXivgr-qc/9603019OpenAlexW2949341344WikidataQ57394261 ScholiaQ57394261MaRDI QIDQ5689701

Jorge Pullin, Rodolfo Gambini

Publication date: 7 January 1997

Published in: Classical and Quantum Gravity (Search for Journal in Brave)

Abstract: We suggest how to interpret the action of the quantum Hamiltonian constraint of general relativity in the loop representation as a skein relation on the space of knots. Therefore, by considering knot polynomials that are compatible with that skein relation, one guarantees that all the quantum Einstein equations are solved. We give a particular example of such invariant and discuss the consistency of the constraint algebra in this approach.

Full work available at URL: https://arxiv.org/abs/gr-qc/9603019

zbMATH Keywords

loop representation skein relation space of knots

Mathematics Subject Classification ID

Quantization of the gravitational field (83C45)

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