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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 registered SciPost users): | Yui Hayashi |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2112.08551v1 (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 (IWHEP2021) |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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)
Reports on this Submission
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.