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

Abstract

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.

arXiv commentAccepted for publication in Phys. Rev. D. 4 pages, revtex4. Corrected typos, and a minor sign changes: in the explicit expression of the action of a special conformal transformation (page 2 v2), in the last expression of Y^H (page 4 v3)

References in corpus (2)

• The Conformal Group SO(4,2) and Robertson-Walker Spacetimes
• Conformally related massless fields in dS, AdS and Minkowski spaces

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