Effective action and semiclassical limit of spin foam models

Details Effective action and semiclassical limit of spin foam models Effective action and semiclassical limit of spin foam models

2011-04-07

arxiv.org/abs/1104.1384v2

Class. Quant. Grav. 28, 225004 (2011)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Improved presentation, 2 references added. 15 pages, no figures

Scientific paper

10.1088/0264-9381/28/22/225004

We define an effective action for spin foam models of quantum gravity by adapting the background field method from quantum field theory. We show that the Regge action is the leading term in the semi-classical expansion of the spin foam effective action if the vertex amplitude has the large-spin asymptotics which is proportional to an exponential function of the vertex Regge action. In the case of the known three-dimensional and four-dimensional spin foam models this amounts to modifying the vertex amplitude such that the exponential asymptotics is obtained. In particular, we show that the ELPR/FK model vertex amplitude can be modified such that the new model is finite and has the Einstein-Hilbert action as its classical limit. We also calculate the first-order and some of the second-order quantum corrections in the semi-classical expansion of the effective action.

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