Hamiltonian variational method for relativistic few-particle systems

The paper gives a short description of using the variational principle for deriving from quantum field theory within the Hamiltonian formalism the wave-equations that describe relativistic few-particle bound or quasi-bound systems. The advantages and disadvantages of the approach are discussed in comparison with the conventional Bethe-Salpeter method. Some examples of applications of the approach are recounted. We describe in more detail a recent application to Higgs model that is defined by the relevant sector of the Standard Model Lagrangian. We study the possible existence of two-Higgs bound states. The trial wave function includes two components representing two and three free Higgs particles. The two coupled integral equations for the unknown coefficient functions follow from the variational principle.In a certain approximation these equations reduce to a single Schroedinger like equation. The effective h - h interaction kernel contains Yukawa- and contact - type interactions. Numerical solution of the equation indicates that l=0 two-Higgs bound states are possible only if Higgs particle turn out to be quite heavy, mH ≥ 894 GeV