Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1996-06-07
Phys.Rev. D55 (1997) 6099-6111
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
24 pages, 21 PostScript figures, uses epsfig.sty, Minor corrections in the final formula in the main body of the paper and in
Scientific paper
10.1103/PhysRevD.55.6099
The evolution of spin network states in loop quantum gravity can be described by introducing a time variable, defined by the surfaces of constant value of an auxiliary scalar field. We regulate the Hamiltonian, generating such an evolution, and evaluate its action both on edges and on vertices of the spin network states. The analytical computations are carried out completely to yield a finite, diffeomorphism invariant result. We use techniques from the recoupling theory of colored graphs with trivalent vertices to evaluate the graphical part of the Hamiltonian action. We show that the action on edges is equivalent to a diffeomorphism transformation, while the action on vertices adds new edges and re-routes the loops through the vertices.
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