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.

The interaction between three photons is studied in de Sitter ambient space formalism. As a special case, the half harmonic generator is considered, i.e., one photon decays to two same-energy photons. The scattering matrix elements are presented which define the indirect gravitational effect on quantum field theory. The null curvature limit of scattering matrix is obtained for comparing it with its Minkowskian counterpart. The Hamiltonian of this interaction, in Minkowski space-time, was presented by using the quantum vacuum fluctuation in the one-loop approximation.

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.

The scalar–spinor interaction Lagrangian is presented by the Yukawa potential. In dS ambient space formalism, the interaction Lagrangian of scalar–spinor fields was obtained from a new transformation which is very similar to the gauge theory. The interaction of massless minimally coupled (mmc) scalar and spinor fields was investigated. The Minkowski limit of the mmc scalar field and massive spinor field interaction in the ambient space formalism of de Sitter spacetime is calculated. The interaction Lagrangian and mmc scalar field in the null curvature limit become zero and the local transformation in the null curvature limit become a constant phase transformation and the interaction in this limit become zero. The covariant derivative reduces to ordinary derivative too. Then, we conclude that this interaction is due to the curvature of spacetime and then the mmc scalar field may be a part of a gravitational field.

The interaction of massless minimally coupled scalar field and spinor field [Formula: see text] is investigated and the behavior of interaction and scattering matrix in Minkowski limit is studied. It is seen that the massless minimally coupled scalar field operator, the interaction Lagrangian and the scattering matrix become zero. Also, the incoming and outgoing spinor fields, which in de Sitter spacetime are different and are interacted with massless minimally coupled scalar field, in null curvature limit are the same and no interaction seen. In other words, the massless minimally coupled scalar field is dependent on curvature and can be considered as a part of a gravitational field.