Partition functions and topology changing amplitudes in the 3-D lattice gravity of Ponzano and Regge
Dec, 199129 pages
Published in:
- Nucl.Phys.B 382 (1992) 276-304
- Published: 1992
e-Print:
- hep-th/9112072 [hep-th]
Report number:
- RIMS-851
View in:
Citations per year
Abstract:
We define a physical Hilbert space for the three-dimensional lattice gravity of Ponzano and Regge and establish its isomorphism to the ones in the Chern-Simons theory. It is shown that, for a handlebody of any genus, a Hartle-Hawking-type wave-function of the lattice gravity transforms into the corresponding state in the Chern-Simons theory under this isomorphism. Using the Heegaard splitting of a three-dimensional manifold, a partition function of each of these theories is expressed as an inner product of such wave-functions. Since the isomorphism preserves the inner products, the partition function of the two theories are the same for any closed orientable manifold. We also discuss on a class of topology-changing amplitudes in the lattice gravity and their relation to the ones in the Chern-Simons theory.- lattice field theory: Regge
- gravitation
- dimension: 3
- Chern-Simons term
- symmetry: ISO(3)
- wave function
- partition function
- linear space: Hilbert space
References(13)
Figures(0)