Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 15 (2019), 060, 22 pages      arXiv:1708.00538      https://doi.org/10.3842/SIGMA.2019.060

Wavepackets on de Sitter Spacetime

João C.A. Barata a and Marcos Brum ab
a) Instituto de Física, Universidade de São Paulo, Rua do Matão 1371, São Paulo, 05508-090, Brasil
b) Departamento de Matemática, Universidade Federal do Rio de Janeiro, Campus Duque de Caxias, Rodovia Washington Luiz Km 104,5, Duque de Caxias, 25265-970, Brazil

Received April 16, 2019, in final form August 12, 2019; Published online August 15, 2019

Abstract
We construct wavepackets on de Sitter spacetime, with masses consistently defined from the eigenvalues of an irreducible representation of a Casimir element in the universal enveloping algebra of the Lorentz algebra and analyse their asymptotic behaviour. Furthermore, we show that, in the limit as the de Sitter radius tends to infinity, the wavepackets tend to the wavepackets of Minkowski spacetime and the plane waves arising after contraction have support sharply located on the mass shell.

Key words: quantum field theory on de Sitter spacetime; Haag-Ruelle scattering theory; theory of group representations; algebraic quantum field theory.

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