On the constant that fixes the area spectrum in canonical quantum gravity
- 1 January 1998
- journal article
- letter
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 15 (1) , L1-L4
- https://doi.org/10.1088/0264-9381/15/1/001
Abstract
The formula for the area eigenvalues 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 times the 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 , where is the spin connection compatible with the triad field, K is the extrinsic curvature and is Immirzi parameter, the value of the multiplicative factor is . In other words, each edge of a spin network contributes an area to any surface it transversely intersects.Keywords
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