Signal propagation on kappa-Minkowski spacetime and nonlocal two-point functions

We study the propagation of quantum fields on kappa-Minkowsi spacetime. Starting from the non-commutative partition function for a free field written in momentum space, we derive the Feynman propagator and analyze the nontrivial singularity structure determined by the group manifold geometry of momentum space. The additional contributions due to such a singularity structure result in a deformed field propagation which can be alternatively described in terms of an ordinary field propagation determined by a source with a blurred spacetime profile. We show that the kappa-deformed Feynman propagator can be written in terms of vacuum expectation values of a commutative nonlocal quantum field. For sub-Planckian modes, the kappa-deformed propagator corresponds to the vacuum expectation value of the time-ordered product of nonlocal field operators while for trans-Plankian modes, this is replaced by the Hadamard two-point function, the vacuum expectation value of the anticommutator of nonlocal field operators.