Form factors, spectral and Källén-Lehmann representation in nonlocal quantum gravity
Abstract We discuss the conical region of convergence of exponential and asymptotically polynomial form factors and their integral representations. Then, we calculate the spectral representation of the propagator of nonlocal theories with entire form factors, in particular, of the above type. The sp...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2024)204 |
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| author | Fabio Briscese Gianluca Calcagni Leonardo Modesto Giuseppe Nardelli |
| author_facet | Fabio Briscese Gianluca Calcagni Leonardo Modesto Giuseppe Nardelli |
| author_sort | Fabio Briscese |
| collection | DOAJ |
| description | Abstract We discuss the conical region of convergence of exponential and asymptotically polynomial form factors and their integral representations. Then, we calculate the spectral representation of the propagator of nonlocal theories with entire form factors, in particular, of the above type. The spectral density is positive-definite and exhibits the same spectrum as the local theory. We also find that the piece of the propagator corresponding to the time-ordered two-point correlation function admits a generalization of the Källén-Lehmann representation with a standard momentum dependence and a spectral density differing from the local one only in the presence of interactions. These results are in agreement with what already known about the free theory after a field redefinition and about perturbative unitarity of the interacting theory. The spectral and Källén-Lehmann representations have the same standard local limit, which is recovered smoothly when sending the fundamental length scale ℓ * in the form factor to zero. |
| format | Article |
| id | doaj-art-b71e3752d24b43888dc82af3322a6f1b |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-b71e3752d24b43888dc82af3322a6f1b2024-11-24T12:07:07ZengSpringerOpenJournal of High Energy Physics1029-84792024-08-012024813110.1007/JHEP08(2024)204Form factors, spectral and Källén-Lehmann representation in nonlocal quantum gravityFabio Briscese0Gianluca Calcagni1Leonardo Modesto2Giuseppe Nardelli3Dipartimento di Architettura, Università Roma TreInstituto de Estructura de la Materia, CSICDipartimento di Fisica, Università di CagliariDipartimento di Matematica e Fisica, Università Cattolica del Sacro CuoreAbstract We discuss the conical region of convergence of exponential and asymptotically polynomial form factors and their integral representations. Then, we calculate the spectral representation of the propagator of nonlocal theories with entire form factors, in particular, of the above type. The spectral density is positive-definite and exhibits the same spectrum as the local theory. We also find that the piece of the propagator corresponding to the time-ordered two-point correlation function admits a generalization of the Källén-Lehmann representation with a standard momentum dependence and a spectral density differing from the local one only in the presence of interactions. These results are in agreement with what already known about the free theory after a field redefinition and about perturbative unitarity of the interacting theory. The spectral and Källén-Lehmann representations have the same standard local limit, which is recovered smoothly when sending the fundamental length scale ℓ * in the form factor to zero.https://doi.org/10.1007/JHEP08(2024)204Classical Theories of GravityModels of Quantum Gravity |
| spellingShingle | Fabio Briscese Gianluca Calcagni Leonardo Modesto Giuseppe Nardelli Form factors, spectral and Källén-Lehmann representation in nonlocal quantum gravity Journal of High Energy Physics Classical Theories of Gravity Models of Quantum Gravity |
| title | Form factors, spectral and Källén-Lehmann representation in nonlocal quantum gravity |
| title_full | Form factors, spectral and Källén-Lehmann representation in nonlocal quantum gravity |
| title_fullStr | Form factors, spectral and Källén-Lehmann representation in nonlocal quantum gravity |
| title_full_unstemmed | Form factors, spectral and Källén-Lehmann representation in nonlocal quantum gravity |
| title_short | Form factors, spectral and Källén-Lehmann representation in nonlocal quantum gravity |
| title_sort | form factors spectral and kallen lehmann representation in nonlocal quantum gravity |
| topic | Classical Theories of Gravity Models of Quantum Gravity |
| url | https://doi.org/10.1007/JHEP08(2024)204 |
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