Bound-state problem in quantum field theory: Linear and nonlinear dynamics

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Abstract
We study bound-state solutions of a simple Lagrangian containing two coupled scalar fields (the Wick-Cutkosky model). In this work we obtain (nontopological) soliton solutions which are nonperturbative in character and which can be studied for large values of the coupling constant. We provide a unified approach to this problem by starting with a Bethe-Salpeter equation and demonstrating that different choices of the kernel will lead to either the usual ‘‘ladder approximation’’ or to the nonlinear equations of the soliton analysis.