A Mellin space approach to cosmological correlators. (English) Zbl 1434.81117
Summary: We propose a Mellin space approach to the evaluation of late-time momentum-space correlation functions of quantum fields in \((d + 1)\)-dimensional de Sitter space. The Mellin-Barnes representation makes manifest the analytic structure of late-time correlators and, more generally, provides a convenient general \(d\) framework for the study of conformal correlators in momentum space. In this work we focus on tree-level correlation functions of general scalars as a prototype, including \(n\)-point contact diagrams and 4-point exchanges. For generic scalars, both the contact and exchange diagrams are given by (generalised) Hypergeometric functions, which reduce to existing expressions available in the literature for \(d = 3\) and external scalars which are either simultaneously conformally coupled or massless. This approach can also be used for the perturbative bulk evaluation of momentum space boundary correlators in \((d + 1)\)-dimensional anti-de Sitter space (Witten diagrams).
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 62P35 | Applications of statistics to physics |
| 81U05 | \(2\)-body potential quantum scattering theory |
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
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