Chiral Symmetry Breaking and Confinement Beyond Rainbow-Ladder Truncation

Abstract

A non-perturbative construction of the 3-point fermion-boson vertex which obeys its Ward-Takahashi or Slavnov-Taylor identity, ensures the massless fermion and boson propagators transform according to their local gauge covariance relations, reproduces perturbation theory in the weak coupling regime and provides a gauge independent description for dynamical chiral symmetry breaking (DCSB) and confinement has been a long-standing goal in physically relevant gauge theories such as quantum electrodynamics (QED) and quantum chromodynamics (QCD). In this paper, we demonstrate that the same simple and practical form of the vertex can achieve these objectives not only in 4-dimensional quenched QED (qQED4) but also in its 3-dimensional counterpart (qQED3). Employing this convenient form of the vertex \emph{ansatz} into the Schwinger-Dyson equation (SDE) for the fermion propagator, we observe that it renders the critical coupling in qQED4 markedly gauge independent in contrast with the bare vertex and improves on the well-known Curtis-Pennington construction. Furthermore, our proposal yields gauge independent order parameters for confinement and DCSB in qQED3.

8 pages, 6 figures

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Cited by in corpus (24)

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• QCD phase transitions via a refined truncation of Dyson-Schwinger equations
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• ${\eta }_c$ Elastic and Transition Form Factors: Contact Interaction and Algebraic Model
• Transverse Takahashi Identities and Their Implications for Gauge Independent Dynamical Chiral Symmetry Breaking
• QCD: Restoration of Chiral Symmetry and Deconfinement for Large N_f
• Existence and stability of multiple solutions to the gap equation
• The QCD phase diagram from Schwinger-Dyson Equations
• Effect of the Quark-Gluon Vertex on Dynamical Chiral Symmetry Breaking
• Multiple solutions for the fermion mass function in QED3
• Fermion and Photon gap-equations in Minkowski space within the Nakanishi Integral Representation method
• A fresh look at the (non-)Abelian Landau-Khalatnikov-Fradkin transformations
• The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking
• Gauge dependence of the quark gap equation: an exploratory study
• Vacuum Polarization and Dynamical Chiral Symmetry Breaking: Phase Diagram of QED with Four-Fermion Contact Interaction
• Electron-Photon Vertex and Dynamical Chiral Symmetry Breaking in Reduced QED: An Advanced Study of Gauge Invariance
• Constructing Scalar-Photon Three Point Vertex in Massless Quenched Scalar QED
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• Extracting a model quark propagator's spectral density
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