Causality and matter propagation in 3d spin foam quantum gravity

Abstract

In this paper we tackle the issue of causality in quantum gravity, in the context of 3d spin foam models. We identify the correct procedure for implementing the causality/orientation dependence restriction that reduces the path integral for BF theory to that of quantum gravity in first order form. We construct explicitly the resulting causal spin foam model. We then add matter degrees of freedom to it and construct a causal spin foam model for 3d quantum gravity coupled to matter fields. Finally, we show that the corresponding spin foam amplitudes admit a natural approximation as the Feynman amplitudes of a non-commutative quantum field theory, with the appropriate Feynman propagators weighting the lines of propagation, and that this effective field theory reduces to usual QFT in flat space in the no-gravity limit.

v2: 26 pages, 2 figures, RevTeX, some typos and some formulae corrected with no relevant change for the results, one reference added

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• A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity
• Quantum Gravity and Matter: Counting Graphs on Causal Dynamical Triangulations
• A Note on B-observables in Ponzano-Regge 3d Quantum Gravity
• Two-point functions in (loop) quantum cosmology
• Group field theory and simplicial quantum gravity
• Encoding simplicial quantum geometry in group field theories
• Emergent matter from 3d generalised group field theories
• Conserved Topological Defects in Non-Embedded Graphs in Quantum Gravity
• Causal structure in spin-foams
• Relativistic Planck-scale polymer
• Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model