A 3d perspective on de Sitter quantum field theory
Published on:
November 08, 2023
Abstract
A basic introduction to scalar field theory in de Sitter spacetime is presented. The focus of this presentation takes place in three-dimensions. I will review the representation theory of $SO(1,3)$, the isometry group of three-dimensional de Sitter space. I will use this representation theory to build scalar fields in the inflationary patch and reproduce their two-point function in the Bunch Davies vacuum. I will then describe analogous calculations in Euclidean signature utilizing the sphere heat-kernel which is exact in three-dimensions. I will also cast the heat-kernel in an alternate description as the quantum mechanics of a particle worldline; in this context, computations will make explicit use of worldlines that wrap the compact Euclidean space, a phenomenon that does not occur in analogous Anti-de Sitter computations. Lastly, I will describe recent results for coupling quantum matter to three-dimensional quantum gravity in the Chern-Simons formalism by bootstrapping intuition from worldline quantum mechanics to Wilson loop operators. These proceedings are an expanded form of a talk given in the introductory session of a workshop on ``Features of a Quantum de Sitter Universe."
DOI: https://doi.org/10.22323/1.436.0129
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