A finite spin-foam-based theory of three and four dimensional quantum gravity

Abstract

Starting from Ooguri's construction for $BF$ theory in three (and four) dimensions, we show how to construct a well defined theory with an infinite number of degrees of freedom. The spin network states that are kept invariant by the evolution operators of the theory are exact solutions of the Hamiltonian constraint of quantum gravity proposed by Thiemann. The resulting theory is the first example of a well defined, finite, consistent, spin-foam based theory in a situation with an infinite number of degrees of freedom. Since it solves the quantum constraints of general relativity it is also a candidate for a theory of quantum gravity. It is likely, however, that the solutions constructed correspond to a spurious sector of solutions of the constraints. The richness of the resulting theory makes it an interesting example to be analyzed by forthcoming techniques that construct the semi-classical limit of spin network quantum gravity.

4 pages, Revtex, 6 figures included with psfig, to appear in PRD

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Cited by in corpus (7)

• Background Independent Quantum Gravity: A Status Report
• The Spin Foam Approach to Quantum Gravity
• Spin Foam Models for Quantum Gravity
• The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Noncommutative geometry induced by spin effects
• Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity