The Basis of the Ponzano-Regge-Turaev-Viro-Ooguri quantum gravity model in the loop representation basis
- Carlo Rovelli()
- Pittsburgh U. and
- Trento U. and
- INFN, Padua
14 pages
Published in:
- Phys.Rev.D 48 (1993) 2702-2707
e-Print:
- hep-th/9304164 [hep-th]
Report number:
- PITT-GR-93-2
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Abstract:
We show that the Hilbert space basis that defines the Ponzano-Regge- Turaev-Viro-Ooguri combinatorial definition of 3-d Quantum Gravity is the same as the one that defines the Loop Representation. We show how to compute lengths in Witten's 3-d gravity and how to reconstruct the 2-d geometry from a state of Witten's theory. We show that the non-degenerate geometries are contained in the Witten's Hilbert space. We sketch an extension of the combinatorial construction to the physical 4-d case, by defining a modification of Regge calculus in which areas, rather than lengths, are taken as independent variables. We provide an expression for the scalar product in the Loop representation in 4-d. We discuss the general form of a nonperturbative quantum theory of gravity, and argue that it should be given by a generalization of Atiyah's topological quantum field theories axioms.- quantum gravity
- dimension: 3
- lattice field theory
- loop space
- phase space
- partition function
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