Quasi-Potential Equations for a Complex Two-Particle System in the Context of Scalar Theories with Self-Action

Within the framework of the covariant simultaneous approach of quantum field theory, a complex system of two identical scalar particles with third- and fourth-order self-action is examined. Explicit forms of the retarded component of the Green's two-time function and of the energy-dependent interaction operator of the system are obtained in the lowest orders of perturbation theory. Three-dimensional quasi-potential equations for the relativistic wave function of a bound state are derived. Based on the results obtained, a complex system of two Higgs bosons is examined.