Rigorous reconstruction of gluon propagator in the presence of complex singularities
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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SciPost
2022-05-01
|
| Series: | SciPost Physics Proceedings |
| Online Access: | https://scipost.org/SciPostPhysProc.6.017 |
| _version_ | 1818242999512989696 |
|---|---|
| author | Yui Hayashi, Kei-Ichi Kondo |
| author_facet | Yui Hayashi, Kei-Ichi Kondo |
| author_sort | Yui Hayashi, Kei-Ichi Kondo |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-12T13:54:09Z |
| format | Article |
| id | doaj.art-c6d1d318d0d649369c54006e3a4739e5 |
| institution | Directory Open Access Journal |
| issn | 2666-4003 |
| language | English |
| last_indexed | 2024-12-12T13:54:09Z |
| publishDate | 2022-05-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics Proceedings |
| spelling | doaj.art-c6d1d318d0d649369c54006e3a4739e52022-12-22T00:22:29ZengSciPostSciPost Physics Proceedings2666-40032022-05-01601710.21468/SciPostPhysProc.6.017Rigorous reconstruction of gluon propagator in the presence of complex singularitiesYui Hayashi, Kei-Ichi KondoIt 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.https://scipost.org/SciPostPhysProc.6.017 |
| spellingShingle | Yui Hayashi, Kei-Ichi Kondo Rigorous reconstruction of gluon propagator in the presence of complex singularities SciPost Physics Proceedings |
| title | Rigorous reconstruction of gluon propagator in the presence of complex singularities |
| title_full | Rigorous reconstruction of gluon propagator in the presence of complex singularities |
| title_fullStr | Rigorous reconstruction of gluon propagator in the presence of complex singularities |
| title_full_unstemmed | Rigorous reconstruction of gluon propagator in the presence of complex singularities |
| title_short | Rigorous reconstruction of gluon propagator in the presence of complex singularities |
| title_sort | rigorous reconstruction of gluon propagator in the presence of complex singularities |
| url | https://scipost.org/SciPostPhysProc.6.017 |
| work_keys_str_mv | AT yuihayashikeiichikondo rigorousreconstructionofgluonpropagatorinthepresenceofcomplexsingularities |