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arXiv · hep-th/9203079

Weaving a classical geometry with quantum threads

Abhay Ashtekar·Carlo Rovelli·Lee Smolin
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Abstract

Results that illuminate the physical interpretation of states of nonperturbative quantum gravity are obtained using the recently introduced loop variables. It is shown that: i) While local operators such as the metric at a point may not be well-defined, there do exist {\it non-local} operators, such as the area of a given 2-surface, which can be regulated diffeomorphism invariantly and which are finite {\it without} renormalization; ii)there exist quantum states which approximate a given flat geometry at large scales, but such states exhibit a discrete structure at the Planck scale; iii) these results are tied together by the fact that the spectra of the operators that measure the areas of surfaces are quantized in integral units of the Planck area.

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Abhay Ashtekar, Carlo Rovelli, Lee Smolin. 1992-03-30. Weaving a classical geometry with quantum threads. https://doi.org/10.1103/physrevlett.69.237

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