The Kauffman bracket and the Jones polynomial in quantum gravity

Details The Kauffman bracket and the Jones polynomial in quantum gravity The Kauffman bracket and the Jones polynomial in quantum gravity

1995-10-25

arxiv.org/abs/gr-qc/9510050v1

Nucl.Phys. B467 (1996) 332-354

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages

Scientific paper

10.1016/0550-3213(96)00106-X

An analysis of the action of the Hamiltonian constraint of quantum gravity on the Kauffman bracket and Jones knot polynomials is proposed. It is explicitely shown that the Kauffman bracket is a formal solution of the Hamiltonian constraint with cosmological constant ($\Lambda$) to third order in $\Lambda$. The calculation is performed in the extended loop representation of quantum gravity. The analysis makes use of the analytical expressions of the knot invariants in terms of the two and three point propagators of the Chern-Simons theory. Some particularities of the extended loop calculus are considered and the implications of the results to the case of the conventional loop representation are discussed.

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