On the energy spectrum of the Bethe-Salpeter equation

The problem of calculating the energy spectrum of a two-fermion bound state within the Bethe-Salpeter formalism is discussed. An expansion of the kernel of the spinor-spinor Bethe-Salpeter equation in the ladder approximation is found in terms of a biorthogonal basis of the generalized Gilbert-Schmidt series for symmetric equations of the Fredholm type. According to this expansion, a new method of solving the Bethe-Salpeter equation and of funding the mass spectrum is proposed. Methodological result of numerical solutions of equations with scalar interaction is presented