Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2003-03-06
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
32 pages
Scientific paper
The most common spin foam models of gravity are widely believed to be discrete path integral quantizations of the Plebanski action. However, their derivation in present formulations is incomplete and lower dimensional simplex amplitudes are left open to choice. Since their large-spin behavior determines the convergence properties of the state-sum, this gap has to be closed before any reliable conclusion about finiteness can be reached. It is shown that these amplitudes are directly related to the path integral measure and can in principle be derived from it, requiring detailed knowledge of the constraint algebra and gauge fixing. In a related manner, minimal requirements of background independence provide non trivial restrictions on the form of an anomaly free measure. Many models in the literature do not satisfy these requirements. A simple model satisfying the above consistency requirements is presented which can be thought of as a spin foam quantization of the Husain--Kuchar model.
Bojowald Martin
Perez Alejandro
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