Feynman-Schwinder representation approach to nonperturbative physics

The Feynman-Schwinger representation provides a convenient framework for the calculation of nonperturbative propagators. In this paper the authors first investigate an analytically solvable case, namely the scalar QED in 0+1 dimension. With this toy model they illustrate how the formalism works. The analytic result for the self energy is compared with the perturbative result. Next, using a {chi}{sup 2} {phi} interaction, they discuss the regularization of various divergences encountered in this formalism. The ultraviolet divergence, which is common in standard perturbative field theory applications, is removed by using a Pauli-Villars regularization. They show that the divergence associated with large values of Feynman-Schwinger parameter s is spurious and it can be avoided by using an imaginary Feynman parameter is