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.
Ward Identities for Scale and Special Conformal Transformations in Inflation
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abstract
We derive the general Ward identities for scale and special conformal transformations in theories of single field inflation. Our analysis is model independent and based on symmetry considerations alone. The identities we obtain are valid to all orders in the slow roll expansion. For special conformal transformations, the Ward identities include a term which is non-linear in the fields that arises due to a compensating spatial reparametrization. Some observational consequences are also discussed.
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Ward identities from large gauge symmetry impose model-independent constraints on renormalizing inflationary loops and non-perturbatively govern the infrared power spectrum evolution.
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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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Fixing the Renormalization of Inflationary Loops via Ward Identities
Ward identities from large gauge symmetry impose model-independent constraints on renormalizing inflationary loops and non-perturbatively govern the infrared power spectrum evolution.