How gauge covariance of the fermion and boson propagators in QED constrain the effective fermion-boson vertex

Abstract

We derive the gauge covariance requirement imposed on the QED fermion-photon three-point function within the framework of a spectral representation for fermion propagators. When satisfied, such requirement ensures solutions to the fermion propagator Schwinger-Dyson equation (SDE) in any covariant gauge with arbitrary numbers of spacetime dimensions to be consistent with the Landau-Khalatnikov-Fradkin transformation (LKFT). The general result has been verified by the special cases of three and four dimensions. Additionally, we present the condition that ensures the vacuum polarization is independent of the gauge parameter. As an illustration, we show how the Gauge Technique dimensionally regularized in 4D does not satisfy the covariance requirement.

arXiv comment14 pages, 5 figures

References in corpus (24)

• Dyson-Schwinger Equations and the Application to Hadronic Physics
• Bethe-Salpeter Study of Vector Meson Masses and Decay Constants
• Collective perspective on advances in Dyson-Schwinger Equation QCD
• Imaging dynamical chiral symmetry breaking: pion wave function on the light front
• Analysis of a quenched lattice-QCD dressed-quark propagator
• Nucleon and Roper electromagnetic elastic and transition form factors
• Structure of the neutral pion and its electromagnetic transition form factor
• Dynamical chiral symmetry breaking and the fermion--gauge-boson vertex
• Confinement Phenomenology in the Bethe-Salpeter Equation
• Gauge independent Chiral Symmetry Breaking in Quenched QED
• Building the Full Fermion-Photon Vertex of QED by Imposing Multiplicative Renormalizability of the Schwinger-Dyson Equations for the Fermion and Photon Propagators
• Solving the Bethe-Salpeter equation for bound states of scalar theories in Minkowski space
• $\bar{q}q$ condensate for light quarks beyond the chiral limit
• Revealing dressed-quarks via the proton's charge distribution
• Study of relativistic bound states for scalar theories in Bethe-Salpeter and Dyson-Schwinger formalism
• Bethe-Salpeter bound-state structure in Minkowski space
• Identical Relations among Transverse Parts of Variant Green Functions and the Full Vertices in Gauge Theories
• Numerical Investigation of Fermion Mass Generation in QED
• Critical Number of Flavours in QED
• Regularization-independent studies of nonperturbative field theory
• Quantum anomaly of the transverse Ward-Takahashi relation for the axial-vector vertex
• Regularization-independent study of renormalized non-perturbative quenched QED
• Strongly-Coupled Unquenched QED4 Propagators Using Schwinger-Dyson Equations
• Running Masses in the Nucleon and its Resonances

Cited by in corpus (11)

• Quark-gluon Vertex: A Perturbation Theory Primer and Beyond
• Non-perturbative aspects of Euclidean Yang-Mills theories in linear covariant gauges: Nielsen identities and a BRST invariant two-point correlation function
• Transverse Takahashi Identities and Their Implications for Gauge Independent Dynamical Chiral Symmetry Breaking
• Landau-Khalatnikov-Fradkin transformation and the mystery of even $\zeta$-values in Euclidean massless correlators
• Exact Solutions to the Fermion Propagator Schwinger-Dyson Equation in Minkowski space with on-shell Renormalization for Quenched QED
• The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking
• Landau-Khalatnikov-Fradkin transformation for the fermion propagator in QED in arbitrary dimensions
• Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED
• Gauge covariance of the fermion Schwinger-Dyson equation in QED
• The Podolsky propagator in gap and bound-state equations
• Dynamical Chiral Symmetry Breaking in Quantum Chromo Dynamics: Delicate and Intricate