Renormalization of the ladder light-front Bethe-Salpeter equation in the Yukawa model - art. no. 064003

The reduction of the two-fermion Bethe-Salpeter equation in the framework o f light-front dynamics is studied for the Yukawa model. It yields auxiliary three-dimensional quantities For the transition matrix and the bound state . The arising effective interaction can be perturbatively expanded in power s of the coupling constant g(s) allowing a defined number of boson exchange s; it is divergent and needs renormalization; it also includes the instanta neous term of the Dirac propagator. One possible solution of the renormaliz ation problem of the boson exchanges is shown to be provided by expanding t he effective interaction beyond single boson exchange. The effective intera ction in ladder approximation up to order g(s)(4) is discussed in detail. I t is shown that the effective interaction naturally yields the "box counter term" required to be introduced ad hoc previously. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxili ary three-dimensional quantities.