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Canonical loop quantum gravity

LQG quantizes Einstein's theory on a space-like foliation a la Dirac. Quantum states represent quantum space hypersurfaces, and geometric quantities like areas, volumes, and angles become operators. The theory predicts that geometric operators have a discrete spectrum and indicates a minimal area of the Planck scale. The theory paints an image of quantum space with a granular and discrete structure. Quantum space can be represented by chunks of space with discrete volumes and discrete areas of the interfaces between them. The states with this enticing geometrical interpretation form the so-called spin network basis of the LQG Hilbert space. Part of my work in LQG focused on this picture.

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