Discreteness of area and volume in quantum gravity

摘要: We study the operator that corresponds to measurement of volume, in non-perturbative quantum gravity, and we compute its spectrum. The is constructed loop representation, via a regularization procedure; it finite, background independent, diffeomorphism-invariant, therefore well defined on space diffeomorphism invariant states (knot states). find spectrum volume any physical region discrete. A family eigenstates are one correspondence with spin networks, which were introduced by Penrose different context. corresponding component spectrum, exhibit eigenvalues explicitly. other related generalization their can be computed diagonalizing finite dimensional matrices. Furthermore, show diagonalize also area operator. argue spectra determined here considered as predictions loop-representation formulation gravity outcomes (hypothetical) Planck-scale sensitive measurements geometry space.