The area spectrum in quantum gravity

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Abstract
We show that, apart from the usual area operator of non-perturbative quantum gravity, there exists another, closely related, operator that measures areas of surfaces. Both corresponding classical expressions yield the area. Quantum mechanically, however, the spectra of the two operators are different, coinciding only in the limit when the spins labelling the state are large. We argue that both operators are legitimate quantum operators, and the choice of which one to use depends on the context of the physical problem of interest. Thus, for example, we argue that it is the operator proposed here that is relevant for use in the context of black holes as measuring the area of the black-hole horizon. We show that the difference between the two operators is due to the non-commutativity that is known to arise in the quantum theory. We give a heuristic picture explaining the difference between the two area spectra in terms of quantum fluctuations of the surface whose area is being measured.

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