Path Integral Quantisation of Finite Noncommutative Geometries

Details Path Integral Quantisation of Finite Noncommutative Geometries Path Integral Quantisation of Finite Noncommutative Geometries

2000-07-05

arxiv.org/abs/gr-qc/0007005v4

J.Geom.Phys. 44 (2002) 115-128

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, LaTeX2e, significantly revised. This is the published version with some minor additions

Scientific paper

We present a path integral formalism for quantising gravity in the form of the spectral action. Our basic principle is to sum over all Dirac operators. The approach is demonstrated on two simple finite noncommutative geometries: the two-point space, and the matrix geometry M_2(C). On the first, the graviton is described by a Higgs field, and on the second, it is described by a gauge field. We start with the partition function and calculate the propagator and Greens functions for the gravitons. The expectation values of distances are evaluated, and we discover that distances shrink with increasing graviton excitations. We find that adding fermions reduces the effects of the gravitational field. A comparison is also made with Rovelli's canonical quantisation approach, and with his idea of spectral path integrals. We include a brief discussion on the quantisation of a Riemannian manifold.

Affiliated with

Also associated with

No associations

Rating

Path Integral Quantisation of Finite Noncommutative Geometries 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 Path Integral Quantisation of Finite Noncommutative Geometries, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Path Integral Quantisation of Finite Noncommutative Geometries will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-171594