Regularization-independent studies of nonperturbative field theory

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.