Asymptotically safe — canonical quantum gravity junction
Abstract The canonical (CQG) and asymptotically safe (ASQG) approach to quantum gravity share to be both non-perturbative programmes. However, apart from that they seem to differ in several aspects such as: 1. Signature: CQG is Lorentzian while ASQG is mostly Euclidian. 2. Background Independence (B...
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2024-10-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP10(2024)013 |
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| author | T. Thiemann |
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| author_sort | T. Thiemann |
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| description | Abstract The canonical (CQG) and asymptotically safe (ASQG) approach to quantum gravity share to be both non-perturbative programmes. However, apart from that they seem to differ in several aspects such as: 1. Signature: CQG is Lorentzian while ASQG is mostly Euclidian. 2. Background Independence (BI): CQG is manifesly BI while ASQG is apparently not. 3. Truncations: CQG is apparently free of truncations while ASQG makes heavy use of them. The purpose of the present work is to either overcome actual differences or to explain why apparent differences are actually absent. Thereby we intend to enhance the contact and communication between the two communities. The focus of this contribution is on conceptual issues rather than deep technical details such has high order truncations. On the other hand the paper tries to be self-contained in order to be useful to researchers from both communities. The point of contact is the path integral formulation of Lorentzian CQG in its reduced phase space formulation which yields the formal generating functional of physical (i.e. gauge invariant) either Schwinger or Feynman N-point functions for (relational) observables. The corresponding effective actions of these generating functionals can then be subjected to the ASQG Wetterich type flow equations which serve in particular to find the rigorous generating fuctionals via the inverse Legendre transform of the fixed pointed effective action. |
| format | Article |
| id | doaj-art-47562480af0c47cabe0aed877cfc2e6e |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-47562480af0c47cabe0aed877cfc2e6e2025-08-20T02:20:38ZengSpringerOpenJournal of High Energy Physics1029-84792024-10-0120241016210.1007/JHEP10(2024)013Asymptotically safe — canonical quantum gravity junctionT. Thiemann0Department of Physics, Friedrich-Alexander University Erlangen-NürnbergAbstract The canonical (CQG) and asymptotically safe (ASQG) approach to quantum gravity share to be both non-perturbative programmes. However, apart from that they seem to differ in several aspects such as: 1. Signature: CQG is Lorentzian while ASQG is mostly Euclidian. 2. Background Independence (BI): CQG is manifesly BI while ASQG is apparently not. 3. Truncations: CQG is apparently free of truncations while ASQG makes heavy use of them. The purpose of the present work is to either overcome actual differences or to explain why apparent differences are actually absent. Thereby we intend to enhance the contact and communication between the two communities. The focus of this contribution is on conceptual issues rather than deep technical details such has high order truncations. On the other hand the paper tries to be self-contained in order to be useful to researchers from both communities. The point of contact is the path integral formulation of Lorentzian CQG in its reduced phase space formulation which yields the formal generating functional of physical (i.e. gauge invariant) either Schwinger or Feynman N-point functions for (relational) observables. The corresponding effective actions of these generating functionals can then be subjected to the ASQG Wetterich type flow equations which serve in particular to find the rigorous generating fuctionals via the inverse Legendre transform of the fixed pointed effective action.https://doi.org/10.1007/JHEP10(2024)013Models of Quantum GravityRenormalization and Regularization |
| spellingShingle | T. Thiemann Asymptotically safe — canonical quantum gravity junction Journal of High Energy Physics Models of Quantum Gravity Renormalization and Regularization |
| title | Asymptotically safe — canonical quantum gravity junction |
| title_full | Asymptotically safe — canonical quantum gravity junction |
| title_fullStr | Asymptotically safe — canonical quantum gravity junction |
| title_full_unstemmed | Asymptotically safe — canonical quantum gravity junction |
| title_short | Asymptotically safe — canonical quantum gravity junction |
| title_sort | asymptotically safe canonical quantum gravity junction |
| topic | Models of Quantum Gravity Renormalization and Regularization |
| url | https://doi.org/10.1007/JHEP10(2024)013 |
| work_keys_str_mv | AT tthiemann asymptoticallysafecanonicalquantumgravityjunction |