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GR: Fachverband Gravitation und Relativitätstheorie

GR 18: Poster

GR 18.4: Poster

Thursday, March 14, 2024, 17:15–18:45, HBR 14: Foyer

Scalar Field on Fuzzy de Sitter Space — •Bojana Brkic¹, Ilija Buric², Maja Buric¹, and Dusko Latas¹ — ¹Faculty of Physics, University of Belgrade, Studentski trg 12 SR-11001 Belgrade, Serbia — ²Department of Physics, University of Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy

First, we introduce (commutative) d-dimensional de Sitter space and write down orthonormal bases of solutions to the Klein-Gordon equation in two sets of coordinates - the usual Poincaré coordinates (η,xⁱ) and another coordinate system (η,yⁱ) that is inspired by noncommutative geometry. It is shown that the natural choice of vacuum in the (η,yⁱ) coordinates is invariant under the de Sitter group and the choice of positive frequency modes that gives rise to the Bunch-Davies vacuum is identified. We compute overlaps between field modes in (η,xⁱ) and (η,yⁱ) coordinates [1]. After that, we give the definition of fuzzy de Sitter space, in particular, its differential geometry and the Laplacian [2]. Our main objective is to find the eigenfunctions of the fuzzy Laplacian. We show that eigenfunctions of the Laplacian on commutative de Sitter space in four dimensions, separated in the (η,yⁱ) coordinates, may be directly ’quantised’ to give eigenfunctions of the fuzzy Laplacian. The special choice of coordinates ensures that no issues due to operator ordering arise in the quantisation process. Also, we consider fuzzy de Sitter space in two dimensions.

[1] B. Allen, Phys. Rev. D 32, 3136 (1985)

[2] B. Brkić et al, Class. Quant. Grav. 39, 115001 (2022)

Keywords: Noncommutative geometry; De Sitter space; Quantum field theory on curved spacetime