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We determine the lowest bound-state pole of the density-density correlator inthe scalar Wick-Cutkosky model where two equal-mass constituents interact viathe exchange of mesons. This is done by employing the worldline representationof field theory together with a variational approximation as in Feynman'streatment of the polaron. Unlike traditional methods based on theBethe-Salpeter equation, self-energy and vertex corrections are (approximately)included as are crossed diagrams. Only vacuum-polarization effects of the heavyparticles are neglected. The well-known instability of the model due toself-energy effects leads to large qualitative and quantitative changescompared to traditional approaches which neglect them. We determine numericallythe critical coupling constant above which no real solutions of the variationalequations exist anymore and show that it is smaller than in the one-body casedue to an induced instability. The width of the bound state above the criticalcoupling is estimated analytically.Comment: 10 pages, 2 figures, LaTeX, published versio

WORLDLINE VARIATIONAL APPROXIMATION: A NEW APPROACH TO THE RELATIVISTIC BINDING PROBLEM