2013/12/12 by Laurent Freidel, Freidel, Laurent, Trevor Rempel +1 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical field theory #Classical mechanics #Computer science #Cosmology and Gravitation Theories #Economics #FOS: Physical sciences #Field (mathematics) #General Relativity and Quantum Cosmology (gr-qc) #Geometry #Gravitation #High Energy Physics - Theory (hep-th) #Mathematical physics #Mathematics #Momentum (technical analysis) #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum gravity #Quantum mechanics #Scalar (mathematics) #Scalar field #Scalar field theory #Scalar theories of gravitation #Space (punctuation) #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.1312.3674
26 pages, 6 figures
arxiv created 2013/12/12 · openalex publication_date 2013/12/12 · arxiv updated 2013/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive an action for scalar quantum field theory with cubic interaction in the context of relative locality. Beginning with the generating functional for standard φ3--theory and the corresponding Feynman rules we modify them to account for the non--trivial geometry of momentum space. These modified rules are then used to reconstruct the generating functional and extract the action for the theory. A method for performing a covariant Fourier transform is then developed and applied to the action. We find that the transformed fields depend implicitly on a fixed point in momentum space with fields based at different points being related by a non-local transformation. The interaction term in the action is also non--local, but the kinetic term can be made local by choosing the base point to be the origin of momentum space.