A Kontorovich-Lebedev-Fourier space is built for (d+1)-dimensional de Sitter correlators from the Casimir operator of SO(1,d+1), producing rational propagators and Feynman rules that turn tree and loop diagrams into spectral integrals and orthogonality relations.
De Sitter Momentum Space
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abstract
We construct a natural and nonperturbative momentum space for quantum field theory on $(d+1)$-dimensional de Sitter (dS) spacetime in the Poincar\'e 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 K\"all\'en-Lehmann spectral decomposition of composite operators, and leads to a group-theoretical method to evaluate loop momentum integrals.
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The four-point wavefunction coefficient for conformally coupled scalars exchanging a massive spinning particle is written in closed form as a hypergeometric function of the s-channel Mandelstam variable times a Legendre polynomial factor using the cosmological Grassmannian.
A graph-tubing combinatorial framework governs the first-order differential equations obeyed by master integrals for massive cosmological correlators in de Sitter space.
citing papers explorer
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Kontorovich-Lebedev-Fourier Space for de Sitter Correlators
A Kontorovich-Lebedev-Fourier space is built for (d+1)-dimensional de Sitter correlators from the Casimir operator of SO(1,d+1), producing rational propagators and Feynman rules that turn tree and loop diagrams into spectral integrals and orthogonality relations.
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Cosmological Collider in the Grassmannian
The four-point wavefunction coefficient for conformally coupled scalars exchanging a massive spinning particle is written in closed form as a hypergeometric function of the s-channel Mandelstam variable times a Legendre polynomial factor using the cosmological Grassmannian.
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Differential Equations for Massive Correlators
A graph-tubing combinatorial framework governs the first-order differential equations obeyed by master integrals for massive cosmological correlators in de Sitter space.