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Peer-reviewedCC BY 4.0Journal of High Energy Physics

Kontorovich-Lebedev-Fourier space for de Sitter correlators

  • Nathan Belrhali1
  • Arthur Poisson1
  • Sébastien Renaux-Petel1
  • Denis Werth1,2,3
  1. 1Sorbonne Université
  2. 2Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)
  3. 3Max Planck-IAS-NTU Center for Particle Physics, Cosmology and Geometry
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Abstract

A bstract : 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 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 SO(1, d + 1) Clebsch-Gordan coefficients.

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Cite

BibTeXRIS
BibTeX
@article{belrhali2026kontorovichlebedevfourier,
  title = {{Kontorovich-Lebedev-Fourier space for de Sitter correlators}},
  author = {Nathan Belrhali and Arthur Poisson and Sébastien Renaux-Petel and Denis Werth},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = oct,
  doi = {10.1007/jhep10(2026)242},
  url = {https://link.springer.com/article/10.1007/JHEP10(2026)242},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Kontorovich-Lebedev-Fourier space for de Sitter correlators
AU  - Nathan Belrhali
AU  - Arthur Poisson
AU  - Sébastien Renaux-Petel
AU  - Denis Werth
PY  - 2026
DA  - 2026/10/23
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep10(2026)242
UR  - https://link.springer.com/article/10.1007/JHEP10(2026)242
AB  - A bstract : 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 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 SO(1, d + 1) Clebsch-Gordan coefficients.
SN  - 1029-8479
ER  -