Solution of the Bethe-Salpeter equation in Minkowski space for a two fermion system

Abstract

The method of solving the Bethe-Salpeter equation in Minkowski space, developed previously for spinless particles, 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. Binding energies are in close agreement with the Euclidean results. Corresponding amplitudes in Minkowski space are obtained.

8 pages, 5 figures. Contribution to the proceedings of the Workshop: Light-Cone 2010, "Relativistic Hadronic and Particle Physics", June 14-18, 2010, Valencia, Spain. To be published in the online journal "Proceedings of Science" - PoS