Implementing causality in the spin foam quantum geometry

Details Implementing causality in the spin foam quantum geometry Implementing causality in the spin foam quantum geometry

2002-10-18

arxiv.org/abs/gr-qc/0210064v3

Nucl.Phys. B663 (2003) 231-279

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex,39 pages,8 figures, v3: minor changes, typos in some formulas corrected, comments added, discussion of results improved

Scientific paper

10.1016/S0550-3213(03)00378-X

We analyse the classical and quantum geometry of the Barrett-Crane spin foam model for four dimensional quantum gravity, explaining why it has to be considering as a covariant realization of the projector operator onto physical quantum gravity states. We discuss how causality requirements can be consistently implemented in this framework, and construct causal transiton amplitudes between quantum gravity states, i.e. realising in the spin foam context the Feynman propagator between states. The resulting causal spin foam model can be seen as a path integral quantization of Lorentzian first order Regge calculus, and represents a link between several approaches to quantum gravity as canonical loop quantum gravity, sum-over-histories formulations, dynamical triangulations and causal sets. In particular, we show how the resulting model can be rephrased within the framework of quantum causal sets (or histories).

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