Taming non-analyticities of QFT observables
Abstract Many observables in quantum field theories are involved non-analytic functions of the parameters of the theory. However, it is expected that they are not arbitrarily wild, but rather have only a finite amount of geometric complexity. This expectation has been recently formalized by a tamene...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP02(2025)009 |
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| author | Thomas W. Grimm Giovanni Ravazzini Mick van Vliet |
| author_facet | Thomas W. Grimm Giovanni Ravazzini Mick van Vliet |
| author_sort | Thomas W. Grimm |
| collection | DOAJ |
| description | Abstract Many observables in quantum field theories are involved non-analytic functions of the parameters of the theory. However, it is expected that they are not arbitrarily wild, but rather have only a finite amount of geometric complexity. This expectation has been recently formalized by a tameness principle: physical observables should be definable in o-minimal structures and their sharp refinements. In this work, we show that a broad class of non-analytic partition and correlation functions are tame functions in the o-minimal structure known as ℝ G $$ {\mathbb{R}}_{\mathcal{G}} $$ — the structure defining Gevrey functions. Using a perturbative approach, we expand the observables in asymptotic series in powers of a small coupling constant. Although these series are often divergent, they can be Borel-resummed in the absence of Stokes phenomena to yield the full partition and correlation functions. We show that this makes them definable in ℝ G $$ {\mathbb{R}}_{\mathcal{G}} $$ and provide a number of motivating examples. These include certain 0-dimensional quantum field theories and a set of higher-dimensional quantum field theories that can be analyzed using constructive field theory. Finally, we discuss how the eigenvalues of certain Hamiltonians in quantum mechanics are also definable in ℝ G $$ {\mathbb{R}}_{\mathcal{G}} $$ . |
| format | Article |
| id | doaj-art-24290d84868443cf82dfde65ec59ae3b |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-24290d84868443cf82dfde65ec59ae3b2025-02-09T12:08:41ZengSpringerOpenJournal of High Energy Physics1029-84792025-02-012025212810.1007/JHEP02(2025)009Taming non-analyticities of QFT observablesThomas W. Grimm0Giovanni Ravazzini1Mick van Vliet2Institute for Theoretical Physics, Utrecht UniversityInstitute for Theoretical Physics, Utrecht UniversityInstitute for Theoretical Physics, Utrecht UniversityAbstract Many observables in quantum field theories are involved non-analytic functions of the parameters of the theory. However, it is expected that they are not arbitrarily wild, but rather have only a finite amount of geometric complexity. This expectation has been recently formalized by a tameness principle: physical observables should be definable in o-minimal structures and their sharp refinements. In this work, we show that a broad class of non-analytic partition and correlation functions are tame functions in the o-minimal structure known as ℝ G $$ {\mathbb{R}}_{\mathcal{G}} $$ — the structure defining Gevrey functions. Using a perturbative approach, we expand the observables in asymptotic series in powers of a small coupling constant. Although these series are often divergent, they can be Borel-resummed in the absence of Stokes phenomena to yield the full partition and correlation functions. We show that this makes them definable in ℝ G $$ {\mathbb{R}}_{\mathcal{G}} $$ and provide a number of motivating examples. These include certain 0-dimensional quantum field theories and a set of higher-dimensional quantum field theories that can be analyzed using constructive field theory. Finally, we discuss how the eigenvalues of certain Hamiltonians in quantum mechanics are also definable in ℝ G $$ {\mathbb{R}}_{\mathcal{G}} $$ .https://doi.org/10.1007/JHEP02(2025)009Nonperturbative EffectsMatrix ModelsSolitons Monopoles and Instantons |
| spellingShingle | Thomas W. Grimm Giovanni Ravazzini Mick van Vliet Taming non-analyticities of QFT observables Journal of High Energy Physics Nonperturbative Effects Matrix Models Solitons Monopoles and Instantons |
| title | Taming non-analyticities of QFT observables |
| title_full | Taming non-analyticities of QFT observables |
| title_fullStr | Taming non-analyticities of QFT observables |
| title_full_unstemmed | Taming non-analyticities of QFT observables |
| title_short | Taming non-analyticities of QFT observables |
| title_sort | taming non analyticities of qft observables |
| topic | Nonperturbative Effects Matrix Models Solitons Monopoles and Instantons |
| url | https://doi.org/10.1007/JHEP02(2025)009 |
| work_keys_str_mv | AT thomaswgrimm tamingnonanalyticitiesofqftobservables AT giovanniravazzini tamingnonanalyticitiesofqftobservables AT mickvanvliet tamingnonanalyticitiesofqftobservables |