Solvable light-front model of a relativistic bound state in 1+1 dimensions

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Abstract
The bound-state equation at equal light-front time is investigated in the framework of a scalar field model in one space and one time dimension in the limit of an infinitely massive exchanged boson. Analytic expressions for the bound-state mass and form factor are obtained. In a weak-binding limit the results for mass and wave function coincide with those based on the nonrelativistic Schrödinger equation with δ-type potential. For weakly bound systems the form factor reduces to the proper static limit in the whole domain of momentum transfers. In general, the quality of the static approximation is controlled by a dimensionless parameter (B¯/m) that characterizes the strength of the binding.