Variational two-particle wave equation in scalar quantum ﬁeld theory - Darewych, J. (Condensed Matter Physics, 2000)
We study two-particle systems in a model quantum ﬁeld theory, in which scalar particles of different mass interact via a mediating scalar ﬁeld. The Lagrangian of the model is reformulated using covariant Green's functions to solve for the mediating ﬁeld in terms of the particle ﬁelds. This results in a Hamiltonian in which the mediating-ﬁeld propagator appears directly in the interaction term. The variational method, with a simple Fock-state trial state, is used to derive a relativistic momentum-space two-particle wave equation. Non-relativistic and one-particle limits of the equation are determined and discussed brieﬂy