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

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

1995-10-25

arxiv.org/abs/gr-qc/9510051v1

Phys.Rev.D53:6966-6978,1996

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages

Scientific paper

10.1103/PhysRevD.53.6966

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 the Hamiltonian does not annihilate the third coefficient of the Jones polynomal ($J_3$) for general extended loops. For ordinary loops the result acquires an interesting geometrical meaning and new possibilities appear for $J_3$ to represent a quantum state of gravity.

Affiliated with

Also associated with

No associations

Rating

Is the third coefficient of the Jones knot polynomial a quantum state of gravity? does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Is the third coefficient of the Jones knot polynomial a quantum state of gravity?, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Is the third coefficient of the Jones knot polynomial a quantum state of gravity? will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-543679