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Feynman-Schwinger representation approach to nonperturbative physics

C. Savkli·J. Tjon·F. Gross
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Abstract

The Feynman-Schwinger representation provides a convenient framework for the cal culation of nonperturbative propagators. In this paper we first investigate an analytically solvable case, namely the scalar QED in 0+1 dimension. With this toy model we illustrate how the formalism works. The analytic result for the self energy is compared with the perturbative result. Next, using a $χ^2ϕ$ interaction, we 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. 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 $is$.

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C. Savkli, J. Tjon, F. Gross. 1999-09-01. Feynman-Schwinger representation approach to nonperturbative physics. https://doi.org/10.1103/physrevc.60.055210%2010.1103%2Fphysrevc.61.069901

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