Covariant dynamics on the energy-momentum space: scalar field theory

Abstract

A scalar field theory is constructed on an energy-momentum background of constant curvature. The generalization of the usual Feynamn rules for the flat geometry follows from the requirement of their covariance. The main result is that the invariant amplitudes are finite at all orders of the perturbation theory, due to the finitness of the momentum space. Finally, the relation with a field theory in spacetime representation is briefly discussed.

References in corpus (6)

• Generalized uncertainty principle or curved momentum space?
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Planck-scale-deformed relativistic symmetries and diffeomorphisms in momentum space
• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• Classical electrodynamics on Snyder space
• Covariant dynamics on the momentum space

Cited by in corpus (1)

• Statistical physics on Euclidean Snyder space: connections with the GUP and cosmological implications