The electron–photon interaction (the spinor–vector field interaction) in the de Sitter ambient space formalism is investigated in the first (leading order) approximation. The interaction Lagrangian and the scattering matrix are presented. In this approximation, the scattering matrix can be written as a expansion of the interaction Lagrangian. The tree-diagram of electron–photon scattering amplitude is calculated. Finally, the Minkowski limit is considered.

In de Sitter ambient space formalism, the massless minimally coupled scalar field can be constructed from a massless conformally coupled scalar field and a constant five-vector [Formula: see text]. Also, a constant five-vector [Formula: see text] appears in the interaction Lagrangian of massless minimally coupled scalar and spinor fields in this formalism. These constant five-vector fields can be fixed in the interaction case in the null curvature limit. Here, we will calculate the [Formula: see text] matrix elements of scalar–spinor field interaction in the tree level approximation. Then the constant five-vectors [Formula: see text] and [Formula: see text], will be fixed by comparing the [Formula: see text] matrix elements in the null curvature limits with the Minkowskian counterparts.