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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