A new viewpoint to Faddeev equations

The inputs for the Faddeev equations, in three-body bound and scattering calculations, are two-body transition operators $t(\epsilon)$. The Lippmann-Schwinger equation should be solved to obtain the matrix elements of $t(\epsilon)$ for negative or positive two-body subsystem energies $\epsilon$, where the values of $\epsilon$ are dictated by the magnitude of Jacobi momentum of the third particle. The solution of the Lippmann-Schwinger equation is challenging, mainly for positive energies where the singularities occur. In this talk, we propose a new form of Faddeev equations for three-body bound state calculations by working directly with two-body interactions and avoiding calculating the matrix elements of two-body $t-$matrices. We test the new formalism in both nonrelativistic and relativistic descriptions of three-body bound states in a three-dimensional approach, without using a partial wave decomposition. The calculated nonrelativistic and relativistic three-body binding energies in the proposed novel Faddeev scheme are in excellent agreement with the results of traditional Faddeev formalism.