On the physical "massless" vector field in de Sitter space

The ”massless” vector field equation in de Sitter (dS) 4-dimensional space is gauge invariant under some special gauge transformations. It is also gauge invariant in ambient space notations in which the field equation is written in terms of the Casimir operators of dS group. In this paper the "massless" vector field equation has been solved in the physical case. It has been shown that the solution can be written as the multiplication of a generalized polarization vector and a ”massless” conformally coupled scalar field in the ambient space notations. The physical vector two-point function has been calculated using ambient space formalism and its zero curvature limit has been considered. It is shown that the physical vector two-point can be written in terms of the conformally coupled massless scalar two-point function in the ambient space notations. The two-point function is expressed in terms of dS intrinsic coor-dinates from its ambient space counterpart, which is dS-invariant and is free from any divergences.