Auxiliary "massless" spin-2 field in de Sitter universe

Abstract

For the tensor field of rank-2 there are two unitary irreducible representation (UIR) in de Sitter (dS) space denoted by ${\Pi }_{2,2}^{\pm }$ and ${\Pi }_{2,1}^{\pm }$ [1]. In the flat limit only the ${\Pi }_{2,2}^{\pm }$ coincides to the UIR of Poincaré group, the second one becomes important in the study of conformal gravity. In the pervious work, Dirac's six-cone formalism has been utilized to obtain conformally invariant (CI) field equation for the "massless" spin-2 field in dS space [2]. This equation results in a field which transformed according to ${\Pi }_{2,1}^{\pm }$, we name this field the auxiliary field. In this paper this auxiliary field is considered and also related two-point function is calculated as a product of a polarization tensor and "massless" conformally coupled scalar field. This two-point function is de Sitter invariant.

16 pages

References in corpus (1)

• "Massless" vector field in de Sitter Universe