2009/03/20 by Florian Girelli, Etera R. Livine, Daniele Oriti · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Commutative property #Cosmology and Gravitation Theories #Formalism (music) #Geometry #Group (periodic table) #Group field theory #Group theory #Mathematical physics #Mathematics #Minkowski space #Noncommutative and Quantum Gravity Theories #Physics #Poincaré group #Pure mathematics #Quantum gravity #Quantum mechanics #Scalar field #Scalar field theory #Spacetime #Symmetry group #Theoretical physics #Theory of relativity #Thermal quantum field theory #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.81.024015
published as Phys.Rev.D81:024015,2010 · 23 pages
arxiv created 2009/03/20 · openalex publication_date 2010/01/15 · arxiv updated 2010/03/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We derive a scalar field theory of the deformed special relativity type, living on noncommutative \ensuremathκ-Minkowski space-time and with a \ensuremathκ-deformed Poincar'e 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.