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Rigorous reconstruction of gluon propagator in the presence of complex singularities

by Yui Hayashi, Kei-Ichi Kondo

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Submission summary

Authors (as Contributors): Yui Hayashi
Submission information
Arxiv Link: (pdf)
Date accepted: 2022-04-19
Date submitted: 2021-12-17 03:43
Submitted by: Hayashi, Yui
Submitted to: SciPost Physics Proceedings
Proceedings issue: XXXIII International Workshop on High Energy Physics (Hard Problems of Hadron Physics: Non-Perturbative QCD & Related Quests)
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


It has been suggested that the Landau-gauge gluon propagator has complex singularities, which invalidates the K\"all\'en-Lehmann spectral representation. Since such singularities are beyond the standard formalism of quantum field theory, the reconstruction of Minkowski propagators from Euclidean propagators has to be carefully examined for their interpretation. In this talk, we present rigorous results on this reconstruction in the presence of complex singularities. As a result, the analytically continued Wightman function is holomorphic in the usual tube, and the Lorentz symmetry and locality are kept valid. On the other hand, the Wightman function on the Minkowski spacetime is a non-tempered distribution and violates the positivity condition. Finally, we discuss an interpretation and implications of complex singularities in quantum theories, arguing that complex singularities correspond to zero-norm confined states.

Published as SciPost Phys. Proc. 6, 017 (2022)

Submission & Refereeing History

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Submission 2112.08551v1 on 17 December 2021

Reports on this Submission

Anonymous Report 1 on 2022-2-25 (Invited Report)


The paper by Y. Hayashi and Kei-Ichi Kondo deals with a very important problem of the relationship of the causal properties of the gluon propagator and its momentum space properties. There were a conviction that the causality does not allow for complex singularities on the 1st Riemannian sheet.
The authors have shown that if to take more general
class of the distributions then causality does not forbid complex sigulariries.
This may have far reaching consequences for string models.

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