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

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.

29 pages, 10 figures; v2: typos corrected, references added

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• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• Tests of Quantum Gravity-Induced Non-Locality: Hamiltonian formulation of a non-local harmonic oscillator
• A group theoretic description of the $\kappa$-Poincaré Hopf algebra
• Quantum particles in non-commutative space-time: an identity crisis
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime
• Noncommutative Lightcones from Quantum SO(2,1) Conformal Groups