Few particle states in quantum field theory. A brief review of the variational approach in the Hamiltonian formalism

We give a brief review of the description of few-particle bound and quasi bound states in quantum field theory (QFT) by means of the variational approach in the Hamiltonian formalism of QFT. After introducing the variational method in Hamiltonian QFT, we discuss two and three body bound states in (N + 1)-dimensional scalar λ φ4 + η φ6 theory, for N=1,2,3. Particle-antiparticle quasi-bound states, that decay into two quanta, as well as three-particle bound states are reviewed for the scalar Yukawa model as well as for QED. Application of the variational Hamiltonian method to meson spectroscopy as well as to the Higgs model is also summarized