Is the third coefficient of the Jones knot polynomial a quantum state of gravity?

Jorge Griego
Phys. Rev. D 53, 6966 – Published 15 June 1996
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Abstract

Some time ago it was conjectured that the coefficients of an expansion of the Jones polynomial in terms of the cosmological constant could provide an infinite string of knot invariants that are solutions of the vacuum Hamiltonian constraint of quantum gravity in the loop representation. Here we discuss the status of this conjecture at third order in the cosmological constant. The calculation is performed in the extended loop representation, a generalization of the loop representation. It is shown that the Hamiltonian does not annihilate the third coefficient of the Jones polynomial (J3) for general extended loops. For ordinary loops the result acquires an interesting geometric meaning and new possibilities appear for J3 to represent a quantum state of gravity. © 1996 The American Physical Society.

  • Received 13 October 1995

DOI:https://doi.org/10.1103/PhysRevD.53.6966

©1996 American Physical Society

Authors & Affiliations

Jorge Griego

  • Instituto de Física, Facultad de Ciencias, Tristán Narvaja 1674, 11200 Montevideo, Uruguay

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Issue

Vol. 53, Iss. 12 — 15 June 1996

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