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arXiv · 1808.02241

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

Michele Arzano·Luca Tiberio Consoli
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Abstract

We study the propagation of quantum fields on $κ$-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 $κ$-deformed Feynman propagator can be written in terms of vacuum expectation values of a commutative non-local quantum field. For sub-Planckian modes the $κ$-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.

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Michele Arzano, Luca Tiberio Consoli. 2018-08-17. Signal propagation on $κ$-Minkowski spacetime and non-local two-point functions. https://doi.org/10.1103/physrevd.98.106018

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