Frederick T. Hawes

Renormalized strong-coupling quenched QED in four dimensions

We study renormalized quenched strong-coupling QED in four dimensions in an arbitrary covariant gauge. Above the critical coupling leading to dynamical chiral symmetry breaking, we show that there is no finite chiral limit. This behavior is found to be independent of the detailed choice of photon-fermion proper vertex in the Dyson-Schwinger equation formalism, provided that the vertex is consistent with the Ward-Takahashi identity and multiplicative renormalizability. We show that the finite solutions previously reported lie in an unphysical regime of the theory with multiple solutions and ultraviolet oscillations in the mass functions. This study is consistent with the assertion that in four dimensions strong coupling QED does not have a continuum limit in the conventional sense. {copyright} {ital 1997} {ital The American Physical Society}

Renormalization and chiral symmetry breaking in quenched QED in arbitrary covariant gauges.

We extend a previous Landau-gauge study of subtractive renormalization of the fermion propagator Dyson-Schwinger equation in strong-coupling, quenched four-dimensional QED to {ital arbitrary} covariant gauges. We use the fermion-photon proper vertex proposed by Curtis and Pennington with an additional correction term included to compensate for the small gauge dependence induced by the ultraviolet regulator. We discuss the chiral limit and the onset of dynamical chiral symmetry breaking in the presence of nonperturbative renormalization. We extract the critical coupling in several different gauges and find evidence of a small residual gauge dependence in this quantity. {copyright} {ital 1996 The American Physical Society.}

Proper vertex in studies of dynamical chiral symmetry breaking

Abstract We examine the importance of the choice of the proper vertex in studies of dynamical symmetry breaking. In particular we compare the effects of including a bare vertex (i.e., rainbow approximation) with those obtained when using the more appropriate Ball-Chiu vertex. In order to quantitatively address this question we have made a detailed numerical comparison in the context of QCD using a variety of assumed nonperturbative behaviors for the effective gluon propagator. From calculations of some relevant physical quantitiess we conclude that approximations to the Ball-Chiu vertex, and especially the bare vertex, tend to underestimate the degree of dynamical chiral symmetry breaking.

Chiral symmetry breaking in strongly coupled quenched QED in four-dimensions using the Dyson-Schwinger equation formalism

We study chiral symmetry breaking in quenched strong-coupling QED4 in arbitrary covariant gauge within the Dyson-Schwinger equation formalism. A recently developed numerical renormalization program is fully implemented. Results are compared for three different fermion-photon proper vertex Ansatze: bare γμ, minimal Ball-Chiu, and Curtis-Pennington. The procedure is straightforward to implement and numerically stable. We discuss the chiral limit and observe that in this limit the renormalized axial current is conserved. A detailed study of residual gauge dependence due to the vertex choice is in progress. The relevance for lattice studies is discussed.