Signal propagation on $\kappa$-Minkowski spacetime and non-local two-point functions

TL;DR

This paper investigates how quantum fields propagate on $$-Minkowski spacetime, revealing a deformed propagation linked to the non-commutative geometry and expressing the propagator through non-local quantum fields.

Contribution

It derives the $$-deformed Feynman propagator from non-commutative partition functions and links it to non-local quantum field operators, highlighting the impact of spacetime non-commutativity.

Findings

Deformed propagator reflects non-trivial singularity structure.

Propagator expressed via vacuum expectation values of non-local fields.

Different behavior for sub-Planckian and trans-Planckian modes.

Abstract

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 non-trivial singularity structure determined by the group manifold geometry of momentum space. The additional contributions due to such 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 non-local quantum field. For sub-Planckian modes the $\kappa$-deformed propagator corresponds to the vacuum expectation value of the time-ordered product of non-local field operators while for trans-Plankian modes this is replaced by the Hadamard two-point function, the vacuum expectation value of the anti-commutator of non-local field operators.