Feynman-Schwinger representation approach to nonperturbative physics - art. no. 055210

The Feynman-Schwinger representation provides a convenient framework for th e calculation of nonperturbative propagators. In this paper we first invest igate an analytically solvable case, namely the scalar QED in 0+1 dimension . With this toy model we illustrate how the formalism works. The analytic r esult for the self-energy is compared with the perturbative result. Next, u sing a chi(2)phi interaction, we discuss the regularization of various dive rgences encountered in this formalism. The ultraviolet divergence, which is common in standard perturbative field theory applications, is removed by u sing a Pauli-Villars regularization. We 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. [S0556-2813(99)03111 -8].