Abstract
We derive a scalar field theory of the deformed special relativity type, living on noncommutative -Minkowski space-time and with a -deformed Poincaré symmetry, from the SO(4,1) group field theory defining the transition amplitudes for topological BF theory in 4 space-time dimensions. This is done at a nonperturbative level of the spin foam formalism working directly with the group field theory (GFT). We show that matter fields emerge from the fundamental model as perturbations around a specific phase of the GFT, corresponding to a solution of the fundamental equations of motion, and that the noncommutative field theory governs their effective dynamics.
- Received 9 July 2009
DOI:https://doi.org/10.1103/PhysRevD.81.024015
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