On the Constant that Fixes the Area Spectrum in Canonical Quantum Gravity

Details On the Constant that Fixes the Area Spectrum in Canonical Quantum Gravity On the Constant that Fixes the Area Spectrum in Canonical Quantum Gravity

1997-09-23

arxiv.org/abs/gr-qc/9709058v1

Class.Quant.Grav.15:L1-L4,1998

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Revtex, 7 pages, no figures

Scientific paper

10.1088/0264-9381/15/1/001

The formula for the area eigenvalues that was obtained by many authors within the approach known as loop quantum gravity states that each edge of a spin network contributes an area proportional to sqrt{j(j+1)} times Planck length squared to any surface it transversely intersects. However, some confusion exists in the literature as to a value of the proportionality coefficient. The purpose of this rather technical note is to fix this coefficient. We present a calculation which shows that in a sector of quantum theory based on the connection A=Gamma-gamma*K, where Gamma is the spin connection compatible with the triad field, K is the extrinsic curvature and gamma is Immirzi parameter, the value of the multiplicative factor is 8*pi*gamma. In other words, each edge of a spin network contributes an area 8*pi*gamma*l_p^2*sqrt{j(j+1)} to any surface it transversely intersects.

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