Further results on geometric operators in quantum gravity

Details Further results on geometric operators in quantum gravity Further results on geometric operators in quantum gravity

1996-12-31

arxiv.org/abs/gr-qc/9612068v1

Class.Quant.Grav. 14 (1997) 1725-1741

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, TeX, 3 figures (epsf)

Scientific paper

10.1088/0264-9381/14/7/010

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

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