Regularization-independent studies of nonperturbative field theory

TL;DR

This paper introduces a regularization-independent approach to study nonperturbative aspects of renormalizable field theories using Dyson-Schwinger equations, demonstrated through quenched QED_4 with analytical and numerical results.

Contribution

It presents a novel regularization-independent method for nonperturbative analysis of field theories via Dyson-Schwinger equations, applied to QED_4 with the Curtis-Pennington vertex.

Findings

Analytical calculation of the mass function at large momenta.

Excellent agreement with previous results for the anomalous mass dimension.

Finite radius of convergence for the perturbation expansion of gamma_m(alpha).

Abstract

We propose a regularization-independent method for studying a renormalizable field theory nonperturbatively through its Dyson-Schwinger equations. Using QED_4 as an example, we show how the coupled equations determining the nonperturbative fermion and photon propagators can be written entirely in terms of renormalized quantities, which renders the equations manifestly finite in a regularization-independent manner. As an illustration of the technique, we apply it to a study of the fermion propagator in quenched QED_4 with the Curtis-Pennington electron-photon vertex. At large momenta the mass function, and hence the anomalous mass dimension gamma_m(alpha), is calculated analytically and we find excellent agreement with previous work. Finally, we show that for the CP vertex the perturbation expansion of gamma_m(alpha) has a finite radius of convergence.