De Sitter Momentum Space
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915941485379584 |
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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 | We construct a natural and nonperturbative momentum space for quantum field theory on $(d+1)$-dimensional de Sitter (dS) spacetime in the Poincaré slicing, adapted to early Universe cosmology. In particular, we identify the dS frequency as the unitary-representation label of the dS isometry group $\mathrm{SO}(1, d+1)$. By diagonalizing the quadratic Casimir together with spatial translations, we provide a harmonic expansion of operators in what we call the Kontorovitch-Lebedev-Fourier (KLF) space. This momentum space shares many structural properties with its Minkowski counterpart, for instance: equations of motion reduce to algebraic equations, and the quadratic dynamics provides a simple propagator analogous to flat space. We reformulate the perturbative computation of in-in correlators in KLF momentum space, showing from first principles how time integrals turn into frequency-space integrals over meromorphic functions. We show how our construction streamlines computations, naturally accommodates the contributions from principal and complementary series in the Källén-Lehmann spectral decomposition of composite operators, and leads to a group-theoretical method to evaluate loop momentum integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15228 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | De Sitter Momentum Space Belrhali, Nathan Poisson, Arthur Renaux-Petel, Sébastien Werth, Denis High Energy Physics - Theory General Relativity and Quantum Cosmology We construct a natural and nonperturbative momentum space for quantum field theory on $(d+1)$-dimensional de Sitter (dS) spacetime in the Poincaré slicing, adapted to early Universe cosmology. In particular, we identify the dS frequency as the unitary-representation label of the dS isometry group $\mathrm{SO}(1, d+1)$. By diagonalizing the quadratic Casimir together with spatial translations, we provide a harmonic expansion of operators in what we call the Kontorovitch-Lebedev-Fourier (KLF) space. This momentum space shares many structural properties with its Minkowski counterpart, for instance: equations of motion reduce to algebraic equations, and the quadratic dynamics provides a simple propagator analogous to flat space. We reformulate the perturbative computation of in-in correlators in KLF momentum space, showing from first principles how time integrals turn into frequency-space integrals over meromorphic functions. We show how our construction streamlines computations, naturally accommodates the contributions from principal and complementary series in the Källén-Lehmann spectral decomposition of composite operators, and leads to a group-theoretical method to evaluate loop momentum integrals. |
| title | De Sitter Momentum Space |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2601.15228 |