Speaker: Denis Werth
De Sitter Momentum Space
In this talk, I will construct a novel frequency-momentum space for de Sitter (dS) correlators from first principles. This construction follows directly from the decomposition into unitary irreducible representations (UIRs) of the spacetime isometry group. While the spatial momentum space is given by the standard Fourier transform, the frequency space arises from diagonalising the quadratic Casimir operator, leading to the Kontorovich-Lebedev-Fourier (KLF) transform.
I will 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 Kallen-Lehmann representation. I will also 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 general 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. At loop level, I will 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鈥揋ordan coefficients.