Feynman-Schwinger representation approach to nonperturbative physics

Details Feynman-Schwinger representation approach to nonperturbative physics Feynman-Schwinger representation approach to nonperturbative physics

1999-06-02

arxiv.org/abs/hep-ph/9906211v2

Phys.Rev. C60 (1999) 055210; Erratum-ibid. C61 (2000) 069901

Physics

High Energy Physics

High Energy Physics - Phenomenology

26 pages, 9 figures, minor correction

Scientific paper

10.1103/PhysRevC.60.055210

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 $\chi^2\phi$ 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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