Graphical Evolution of Spin Network States

Details Graphical Evolution of Spin Network States Graphical Evolution of Spin Network States

1996-06-07

arxiv.org/abs/gr-qc/9606013v3

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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