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

1 APC - THEORIE
APC (UMR_7164) - AstroParticule et Cosmologie, Institut für theoretische Physik
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 to take the point of view of a Minkowskian observer who sees the effect of curvature through additional terms.
Document type :
Journal articles
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http://hal.in2p3.fr/in2p3-00221480
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Submitted on : Monday, January 28, 2008 - 5:35:01 PM
Last modification on : Wednesday, October 21, 2020 - 4:32:12 PM

### Citation

E. Huguet, J. Queva, J. Renaud. Revisiting the conformal invariance of the scalar field: from Minkowski space to de Sitter space. Physical Review D, American Physical Society, 2008, 77, pp.044025. ⟨10.1103/PhysRevD.77.044025⟩. ⟨in2p3-00221480⟩

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