Scalar Field Theory in Curved Momentum Space
Abstract
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 $\varphi^3$theory and the corresponding Feynman rules we modify them to account for the nontrivial 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 nonlocal transformation. The interaction term in the action is also nonlocal, but the kinetic term can be made local by choosing the base point to be the origin of momentum space.
 Publication:

arXiv eprints
 Pub Date:
 December 2013
 DOI:
 10.48550/arXiv.1312.3674
 arXiv:
 arXiv:1312.3674
 Bibcode:
 2013arXiv1312.3674F
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 26 pages, 6 figures