We investigate some properties of geometric operators in canonical quantum gravity in\ud the connection approach `a la Ashtekar, which are associated with volume, area and length\ud of spatial regions. We motivate the construction of analogous discretized lattice quantities,\ud compute various quantum commutators of the type [area,volume], [area,length] and [volume,\ud length], and find they are generally non-vanishing.\ud Although our calculations are performed mostly within a lattice-regularized approach,\ud some are – for special, fixed spin-network configurations – identical with corresponding continuum\ud computations. Comparison with the structure of the discretized theory leads us to\ud conclude that anomalous commutators may be a general feature of operators constructed\ud along similar lines within a continuum loop representation of quantum general relativity. –\ud The validity of the lattice approach remains unaffected
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