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• W2104041846 abstract "We study the operator that corresponds to the measurement of volume, in non-perturbative quantum gravity, and we compute its spectrum. The operator is constructed in the loop representation, via a regularization procedure; it is finite, background independent, and diffeomorphism-invariant, and therefore well defined on the space of diffeomorphism invariant states (knot states). We find that the spectrum of the volume of any physical region is discrete. A family of eigenstates are in one to one correspondence with the spin networks, which were introduced by Penrose in a different context. We compute the corresponding component of the spectrum, and exhibit the eigenvalues explicitly. The other eigenstates are related to a generalization of the spin networks, and their eigenvalues can be computed by diagonalizing finite dimensional matrices. Furthermore, we show that the eigenstates of the volume diagonalize also the area operator. We argue that the spectra of volume and area determined here can be considered as predictions of the loop-representation formulation of quantum gravity on the outcomes of (hypothetical) Planck-scale sensitive measurements of the geometry of space." @default.
• W2104041846 created "2016-06-24" @default.
• W2104041846 creator A5033243912 @default.
• W2104041846 creator A5050105545 @default.
• W2104041846 date "1995-05-01" @default.
• W2104041846 modified "2023-10-03" @default.
• W2104041846 title "Discreteness of area and volume in quantum gravity" @default.
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• W2104041846 doi "https://doi.org/10.1016/0550-3213(95)00150-q" @default.
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