Eigensolutions of the light-cone equation for a scalar field model

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Abstract
The ladder approximation to the bound-state equation at equal light-cone time is investigated in the framework of a scalar field theory. With the help of the Fock transformation the equation is reduced to an eigenvalue problem for a compact operator. Eigensolutions for lowest-energy levels are found and compared with the results of the covariant ladder approximation. In the positronium region both schemes yield equivalent eigenvalues, in agreement with predictions of perturbation theory. For strongly bound systems, however, both schemes give different results. The eigenfunctions are explicitly given and their asymptotic behavior is analyzed.

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