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Hilbert space of quantum field theory in de Sitter spacetime

Joao Penedones1,*, Kamran Salehi Vaziri1,2,†, and Zimo Sun3,‡

  • *Contact author: joao.penedones@epfl.ch
  • †Contact author: k.salehivaziri@uva.nl
  • ‡Contact author: zs8479@princeton.edu
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Phys. Rev. D 111, 045001 – Published 4 February, 2025

DOI: https://doi.org/10.1103/PhysRevD.111.045001

Abstract

We study the decomposition of the Hilbert space of quantum field theory in (d+1)-dimensional de Sitter spacetime into unitary irreducible representations (UIRs) of its isometry group SO(1,d+1). First, we consider multiparticle states in free theories starting from the tensor product of single-particle UIRs. Second, we study conformal multiplets of a bulk conformal field theory with symmetry group SO(2,d+1). Our main tools are the Harish-Chandra characters and the numerical diagonalization of the (truncated) quadratic Casimir of SO(1,d+1). We introduce a continuous density that encodes the spectrum of irreducible representations contained in a reducible one of SO(1,d+1). Our results are complete for d=1 and d=2. In higher dimensions, we rederive and extend several results previously known in the literature. Our work provides the foundation for future nonperturbative bootstrap studies of quantum field theory in de Sitter spacetime.

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Phys. Rev. D 111, 045001– Published 4 February, 2025
  • Received 27 September 2024
  • Accepted 12 December 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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