## Abstract

In the quenched approximation, the gauge covariance properties of three vertex Ansa$iuml-tze in the Schwinger-Dyson equation for the fermion self-energy are analyzed in three- and four-dimensional quantum electrodynamics. Based on the Cornwall-Jackiw-Tomboulis effective action, it is inferred that the spectral representation used for the vertex in the gauge technique cannot support dynamical chiral symmetry breaking. A criterion for establishing whether a given Ansatz can confer gauge covariance upon the Schwinger-Dyson equation is presented and the Curtis and Pennington Ansatz is shown to satisfy this constraint. We obtain an analytic solution of the Schwinger-Dyson equation for quenched, massless three-dimensional quantum electrodynamics for arbitrary values of the gauge parameter in the absence of dynamical chiral symmetry breaking.

Original language | English |
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Pages (from-to) | 5581-5588 |

Number of pages | 8 |

Journal | Physical Review D |

Volume | 47 |

Issue number | 12 |

DOIs | |

Publication status | Published - 1993 |