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The Bethe-Salpeter equation for Wick-Cutkosky-like models is solved in the dressed ladder approximation. The bare vertex truncation of the Dyson-Schwinger equations for propagators is combined with the dressed ladder Bethe-Salpeter equation for the scalar S-wave bound state amplitudes. With the help of the spectral representation the results are obtained directly in Minkowski space. We give a new analytic formula for the resulting equation simplifying the numerical treatment. The bare ladder approximation of the Bethe-Salpeter equation is compared with the one with dressed ladder. The elastic electromagnetic form factors are calculated within the relativistic impulse approximation.

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The role of unitary equivalence of relativistic corrections in elastic electron deuteron scattering is studied, starting from a class of approximately, unitarily equivalent Hamiltonians and using consistent charge density operators. The connection of various formal approaches for deriving the relativistic corrections to wave functions and operators are discussed in detail. For reasons of simplicity, we have chosen a pure one-pion-exchange model and calculated the charge and quadrupole form factors of the deuteron. The numerical results show that the unitary equivalence holds at small momentum transfers, but breaks down rather soon with increasing momentum transfers (& 5 fm~).PACS number(s): 21.45.+v, 25.30.Hf, 13.40.Fn

The normalization condition for the relativistic three nucleon Bethe-Salpeter and Gross bound state vertex functions is derived, for the first time, directly from the three body wave equations. It is also shown that the relativistic normalization condition for the two body Gross bound state vertex function is identical to the requirement that the bound state charge be conserved, proving that charge is automatically conserved by this equation.Comment: 24 pages, 9 figures, published version, minor typos correcte