Finiteness and Dual Variables for Lorentzian Spin Foam Models

Details Finiteness and Dual Variables for Lorentzian Spin Foam Models Finiteness and Dual Variables for Lorentzian Spin Foam Models

2005-08-20

arxiv.org/abs/gr-qc/0508088v2

Class.Quant.Grav. 23 (2006) 701-720

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, 1 figure

Scientific paper

10.1088/0264-9381/23/3/010

We describe here some new results concerning the Lorentzian Barrett-Crane model, a well-known spin foam formulation of quantum gravity. Generalizing an existing finiteness result, we provide a concise proof of finiteness of the partition function associated to all non-degenerate triangulations of 4-manifolds and for a class of degenerate triangulations not previously shown. This is accomplished by a suitable re-factoring and re-ordering of integration, through which a large set of variables can be eliminated. The resulting formulation can be interpreted as a ``dual variables'' model that uses hyperboloid variables associated to spin foam edges in place of representation variables associated to faces. We outline how this method may also be useful for numerical computations, which have so far proven to be very challenging for Lorentzian spin foam models.

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