General Relativity in terms of Dirac Eigenvalues

Details General Relativity in terms of Dirac Eigenvalues General Relativity in terms of Dirac Eigenvalues

1996-12-13

arxiv.org/abs/gr-qc/9612034v1

Phys.Rev.Lett. 78 (1997) 3051-3054

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages, RevTex

Scientific paper

10.1103/PhysRevLett.78.3051

The eigenvalues of the Dirac operator on a curved spacetime are diffeomorphism-invariant functions of the geometry. They form an infinite set of ``observables'' for general relativity. Recent work of Chamseddine and Connes suggests that they can be taken as variables for an invariant description of the gravitational field's dynamics. We compute the Poisson brackets of these eigenvalues and find them in terms of the energy-momentum of the eigenspinors and the propagator of the linearized Einstein equations. We show that the eigenspinors' energy-momentum is the Jacobian matrix of the change of coordinates from metric to eigenvalues. We also consider a minor modification of the spectral action, which eliminates the disturbing huge cosmological term and derive its equations of motion. These are satisfied if the energy momentum of the trans Planckian eigenspinors scale linearly with the eigenvalue; we argue that this requirement approximates the Einstein equations.

Affiliated with

Also associated with

No associations

Rating

General Relativity in terms of Dirac Eigenvalues 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 General Relativity in terms of Dirac Eigenvalues, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and General Relativity in terms of Dirac Eigenvalues will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-332043