Gravity from Dirac Eigenvalues

Details Gravity from Dirac Eigenvalues Gravity from Dirac Eigenvalues

1997-08-19

arxiv.org/abs/gr-qc/9708041v2

Mod.Phys.Lett. A13 (1998) 479-494

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

An enlarged and improved version which will be pubblished in Mod. Phys. Lett. A

Scientific paper

10.1142/S0217732398000541

We study a formulation of euclidean general relativity in which the dynamical variables are given by a sequence of real numbers $\lambda_{n}$, representing the eigenvalues of the Dirac operator on the curved spacetime. These quantities are diffeomorphism-invariant functions of the metric and they form an infinite set of ``physical observables'' for general relativity. Recent work of Connes and Chamseddine suggests that they can be taken as natural variables for an invariant description of the dynamics of gravity. We compute the Poisson brackets of the $\lambda_{n}$'s, and find that these can be expressed in terms of the propagator of the linearized Einstein equations and the energy-momentum of the eigenspinors. We show that the eigenspinors' energy-momentum is the Jacobian matrix of the change of coordinates from the metric to the $\lambda_{n}$'s. We study a variant of the Connes-Chamseddine spectral action which eliminates a disturbing large cosmological term. We analyze the corresponding equations of motion and find that these are solved if the energy momenta of the eigenspinors scale linearly with the mass. Surprisingly, this scaling law codes Einstein's equations. Finally we study the coupling to a physical fermion field.

Affiliated with

Also associated with

No associations

Rating

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

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-294437