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

Kirill Krasnov
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Abstract

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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Kirill Krasnov. 1997-09-23. On the Constant that Fixes the Area Spectrum in Canonical Quantum Gravity. https://doi.org/10.1088/0264-9381%2F15%2F1%2F001

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