General Relativity and Gravitation

, Volume 25, Issue 1, pp 1–6

How the Jones polynomial gives rise to physical states of quantum general relativity

  • Bernd Brügmann
  • Rodolfo Gambini
  • Jorge Pullin
Research Articles

DOI: 10.1007/BF00756923

Cite this article as:
Brügmann, B., Gambini, R. & Pullin, J. Gen Relat Gravit (1993) 25: 1. doi:10.1007/BF00756923


Solutions to both the diffeomorphism and the hamiltonian constraint of quantum gravity have been found in the loop representation, which is based on Ashtekar's new variables. While the diffeomorphism constraint is easily solved by considering loop functionals which are knot invariants, there remains the puzzle why several of the known knot invariants are also solutions to the hamiltonian constraint. We show how the Jones polynomial gives rise to an infinite set of solutions to all the constraints of quantum gravity thereby illuminating the structure of the space of solutions and suggesting the existance of a deep connection between quantum gravity and knot theory at a dynamical level.

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • Bernd Brügmann
    • 1
  • Rodolfo Gambini
    • 2
  • Jorge Pullin
    • 3
  1. 1.Physics DepartmentSyracuse UniversitySyracuseUSA
  2. 2.Facultad de CienciasInstituto de FisicaMontevideoUruguay
  3. 3.Department of PhysicsUniversity of UtahSalt Lake CityUSA