Solving the Bethe-Salpeter equation for two fermions in Minkowski space |
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Authors: | J Carbonell and V A Karmanov |
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Institution: | 1.Laboratoire de Physique Subatomique et Cosmologie, CNRS/IN2P3,Grenoble,France;2.Lebedev Physical Institute,Moscow,Russia |
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Abstract: | The method of solving the Bethe-Salpeter equation in Minkowski space, developed previously for spinless particles (V.A. Karmanov,
J. Carbonell, Eur. Phys. J. A 27, 1 (2006)), is extended to a system of two fermions. The method is based on the Nakanishi integral representation of the
amplitude and on projecting the equation on the light-front plane. The singularities in the projected two-fermion kernel are
regularized without modifying the original BS amplitudes. The numerical solutions for the J = 0 bound state with the scalar, pseudoscalar and massless vector exchange kernels are found. The stability of the scalar
and positronium states without vertex form factor is discussed. Binding energies are in close agreement with the Euclidean
results. Corresponding amplitudes in Minkowski space are obtained. |
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