On the Equivalence between Euclidean and In-In Formalisms in de Sitter QFT

          @misc{ scivideos_PIRSA:10100070,
            doi = {10.48660/10100070},
            url = {https://pirsa.org/10100070},
            author = {Higuchi, Atsushi},
            keywords = {Cosmology},
            language = {en},
            title = { On the Equivalence between Euclidean and In-In Formalisms in de Sitter QFT},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2010},
            month = {oct},
            note = {PIRSA:10100070 see, \url{https://scivideos.org/index.php/pirsa/10100070}}
          }
          

Abstract

We study the relation between two sets of correlators in interacting quantum field theory on de Sitter space. The first are correlators computed using in-in perturbation theory in the region of de Sitter space to the future of a cosmological horizon (also known as the expanding cosmological patch, the conformal patch, or the Poincare patch), and for which the free propagators are taken to be those of the free Euclidean vacuum. The second are correlators obtained by analytic continuation from interacting QFT on Euclidean de Sitter; i.e., they are correlators in the Hartle-Hawking vacuum. We give an analytic argument that these correlators coincide for interacting massive scalar fields with any positive mass. We also verify this result via direct analytical and numerical calculation in two simple examples. The correspondence holds diagram by diagram, and at any finite value of a Pauli-Villars regulator mass M. Along the way, we note interesting connections between various prescriptions for perturbation theory in general static spacetimes with bifurcate Killing horizons.