M Carfora and A Marzuoli 1992 Class. Quantum Grav. 9 595 doi:10.1088/0264-9381/9/3/005
Bounded geometries and topology fluctuations in lattice quantum gravity
M Carfora and A Marzuoli
Show affiliationsThe authors exploit the coarse classification of Riemannian geometries provided by Gromov's pre-compactness theorem (1981) in order to give a rigorous characterization of the partition function of n-dimensional, (n>or=2), lattice quantum gravity. They prove that the resulting theory admits a continuum limit describing phase transitions between different homotopy types of manifolds, with phases parametrized by the fundamental group and by the (Whitehead) torsions of the manifolds sampled. They also show that the results obtained coincide, when specialized to dimension two, with those of two-dimensional quantum gravity models based on random triangulations of surfaces.
- PACS
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04.60.Nc Lattice and discrete methods
04.60.Pp Loop quantum gravity, quantum geometry, spin foams
04.50.-h Higher-dimensional gravity and other theories of gravity
- MSC
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83E15 Kaluza-Klein and other higher-dimensional theories
83C27 Lattice gravity, Regge calculus and other discrete methods
- Subjects
- Dates
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Issue 3 (March 1992)
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Bounded geometries and topology fluctuations in lattice quantum gravity
M Carfora and A Marzuoli 1992 Class. Quantum Grav. 9 595
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