Revisiting the conformal invariance of the scalar field: from Minkowski space to de Sitter space

Details Revisiting the conformal invariance of the scalar field: from Minkowski space to de Sitter space Revisiting the conformal invariance of the scalar field: from Minkowski space to de Sitter space

2008-01-24

arxiv.org/abs/0801.3769v3

Phys.Rev.D77:044025,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Accepted for publication in Phys. Rev. D. 4 pages, revtex4. Corrected typos, and a minor sign changes: in the explicit express

Scientific paper

10.1103/PhysRevD.77.044025

In this article, we clarify the link between the conformal (i.e. Weyl) correspondence from the Minkowski space to the de Sitter space and the conformal (i.e. SO(2,$d$)) invariance of the conformal scalar field on both spaces. We exhibit the realization on de Sitter space of the massless scalar representation of SO$(2,d)$. It is obtained from the corresponding representation in Minkowski space through an intertwining operator inherited from the Weyl relation between the two spaces. The de Sitter representation is written in a form which allows one to take the point of view of a Minkowskian observer who sees the effect of curvature through additional terms.

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