Kontorovich-Lebedev-Fourier Space for de Sitter Correlators
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917414296354816 |
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| author | Belrhali, Nathan Poisson, Arthur Renaux-Petel, Sébastien Werth, Denis |
| author_facet | Belrhali, Nathan Poisson, Arthur Renaux-Petel, Sébastien Werth, Denis |
| contents | In this work, we build a novel frequency-momentum space for $(d+1)$-dimensional de Sitter (dS) correlators from first principles. This construction follows directly from the decomposition into unitary irreducible representations (UIRs) of the spacetime isometry group $\mathrm{SO}(1,d+1)$. While the spatial momentum space is given by the standard $d$-dimensional Fourier transform, the frequency space arises from diagonalising the quadratic Casimir operator, leading to the $(d+1)$-dimensional Kontorovich-Lebedev-Fourier (KLF) transform. We show that square-integrable functions decompose only along the principal series, whereas more general functions can receive discrete contributions from other UIRs. Applying this framework to the bulk CFT two-point function reproduces its Källén-Lehmann representation. Using the path integral formulation, we derive the Feynman rules for in-in perturbation theory in KLF space, leading to the introduction of KLF-space correlators, which are simply related to late-time correlation functions through a reduction formula. Furthermore, the KLF-space formulation sheds light on the simple mathematical structure of perturbative computations. In particular, the propagators take the form of simple rational functions, and tree-level diagrams can be written as spectral integrals over known meromorphic functions, as demonstrated in the example of the single-exchange four-point function. At the loop level, we show, through the example of the self-energy correction to the scalar propagator, that the group-theoretical nature of the construction allows the momentum integral to be recast as an orthogonality relation among $\mathrm{SO}(1,d+1)$ Clebsch-Gordan coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15251 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Kontorovich-Lebedev-Fourier Space for de Sitter Correlators Belrhali, Nathan Poisson, Arthur Renaux-Petel, Sébastien Werth, Denis High Energy Physics - Theory General Relativity and Quantum Cosmology In this work, we build a novel frequency-momentum space for $(d+1)$-dimensional de Sitter (dS) correlators from first principles. This construction follows directly from the decomposition into unitary irreducible representations (UIRs) of the spacetime isometry group $\mathrm{SO}(1,d+1)$. While the spatial momentum space is given by the standard $d$-dimensional Fourier transform, the frequency space arises from diagonalising the quadratic Casimir operator, leading to the $(d+1)$-dimensional Kontorovich-Lebedev-Fourier (KLF) transform. We show that square-integrable functions decompose only along the principal series, whereas more general functions can receive discrete contributions from other UIRs. Applying this framework to the bulk CFT two-point function reproduces its Källén-Lehmann representation. Using the path integral formulation, we derive the Feynman rules for in-in perturbation theory in KLF space, leading to the introduction of KLF-space correlators, which are simply related to late-time correlation functions through a reduction formula. Furthermore, the KLF-space formulation sheds light on the simple mathematical structure of perturbative computations. In particular, the propagators take the form of simple rational functions, and tree-level diagrams can be written as spectral integrals over known meromorphic functions, as demonstrated in the example of the single-exchange four-point function. At the loop level, we show, through the example of the self-energy correction to the scalar propagator, that the group-theoretical nature of the construction allows the momentum integral to be recast as an orthogonality relation among $\mathrm{SO}(1,d+1)$ Clebsch-Gordan coefficients. |
| title | Kontorovich-Lebedev-Fourier Space for de Sitter Correlators |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2604.15251 |