Authors Referees APS Members |
December 2007, to be published in Physical Review D15
Revisiting the conformal invariance of the scalar field: From Minkowski
space to de Sitter space
In this article, we clarify the link between the conformal (\ie~Weyl) correspondence from the Minkowski space to the de Sitter space and the conformal (\ie~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. © 2008 The American Physical Society.
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