Abstract
The scalar Yukawa model, in which a complex scalar field, ϕ, interacts via a real scalar field, χ, is reduced by using covariant Green functions. It is shown that exact few-particle eigenstates of the truncated QFT Hamiltonian can be obtained in the FeshbachVillars formulation if an unorthodox "empty" vacuum state is used. Analytic solutions for the two-body case are obtained for massless chion exchange in 3+1 dimensions and for massive chion exchange in 1+1 dimensions. Comparison is made to ladder BetheSalpeter, FeynmanSchwinger, and quasipotential results for massive chion exchange in 3+1. Equations for the three-body case are also obtained. PACS Nos.: 11.10.Ef, 11.10.Qr, and 03.70.+k
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