The physical hamiltonian in nonperturbative quantum gravity

Details The physical hamiltonian in nonperturbative quantum gravity The physical hamiltonian in nonperturbative quantum gravity

1993-08-05

arxiv.org/abs/gr-qc/9308002v1

Phys.Rev.Lett.72:446-449,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex, 11 pages, no figures, CGPG/93/2

Scientific paper

10.1103/PhysRevLett.72.446

A quantum hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop representation, and is shown to be finite and diffeomorphism invariant. The problem of constructing this hamiltonian is reduced to a combinatorial and algebraic problem which involves the rearrangements of lines through the vertices of arbitrary graphs. This procedure also provides a construction of the hamiltonian constraint as a finite operator on the space of diffeomorphism invariant states as well as a construction of the operator corresponding to the spatial volume of the universe.

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