Looking at QED with Dyson-Schwinger equations: basic equations, Ward-Takahashi identities and the two-photon-two-fermion irreducible vertex
arXiv:2204.04197 · doi:10.1007/s00601-023-01846-5
Abstract
A minimal truncated set of the integral Dyson-Schwinger equations, in Minkowski spacetime, that allows to explore QED beyond its perturbative solution is derived for general linear covariant gauges. The minimal set includes the equations for the fermion and photon propagators, the photon-fermion vertex, and the two-photon-two-fermion one-particle-irreducible diagram. If the first three equations are exact, to build a closed set of equations, the two-photon-two-fermion equation is truncated ignoring the contribution of Green functions with large number of external legs. It is shown that the truncated equation for the two-photon-two-fermion vertex reproduces the lowest-order perturbative result in the limit of the small coupling constant. Furthermore, this equation allows to define an iterative procedure to compute higher order corrections in the coupling constant. The Ward-Takahashi identity for the two-photon-two-fermion irreducible vertex is derived and solved in the soft photon limit, where one of the photon momenta vanish, in the low photon momenta limit and for general kinematics. The solution of the Ward-Takahashi identity determines the longitudinal component of the two-photon-two-fermion irreducible vertex, while it is proposed to use the Dyson-Schwinger equation to determine the transverse part of this irreducible diagram. The two-photon-two-fermion DSE is solved in heavy fermion limit, considering a simplified version of the QED vertices. The contribution of this irreducible vertex to a low-energy effective photon-fermion vertex is discussed and the fermionic operators that are generated are computed in terms of the fermion propagator functions.
arXiv commentVersion accepted for publication in Few Body Syst
References in corpus (48)
- Dyson-Schwinger Equations and the Application to Hadronic Physics
- The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
- New Developments in FeynCalc 9.0
- Unraveling hadron structure with generalized parton distributions
- FeynCalc 9.3: New features and improvements
- Infrared Properties of QCD from Dyson-Schwinger equations
- Theory of deeply virtual Compton scattering on the nucleon
- Introduction to the functional RG and applications to gauge theories
- Observation of exclusive DVCS in polarized electron beam asymmetry measurements
- Review of two-photon exchange in electron scattering
- Theory of the 2S-2P Lamb shift and 2S hyperfine splitting in muonic hydrogen
- Dynamical Chiral Symmetry Breaking in Unquenched
- Radiation reaction in electron-beam interactions with high-intensity lasers
- The proton charge radius
- Higher order proton structure corrections to the Lamb shift in muonic hydrogen
- Two-photon exchange in elastic electron-proton scattering
- Chiral symmetry breaking with lattice propagators
- Deep Inelastic Scattering from off-Shell Nucleons
- ONE LOOP QED VERTEX IN ANY COVARIANT GAUGE: ITS COMPLETE ANALYTIC FORM
- Quark-gluon vertex in arbitrary gauge and dimension
- Hard Two-Photon Contribution to Elastic Lepton-Proton Scattering: Determined by the OLYMPUS Experiment
- Gauge independent Chiral Symmetry Breaking in Quenched QED
- Probing vacuum polarization effects with high-intensity lasers
- Delbrück scattering at energies 140 - 450 MeV
- Quark propagator with two flavors of O(a)-improved Wilson fermions
- The non-perturbative three-point vertex in massless quenched QED and perturbation theory constraints
- Dynamical mass generation in QED with magnetic fields: arbitrary field strength and coupling constant
- Muon : A review
- Virtual Compton scattering off the nucleon at low energies
- Emergence of mass in the gauge sector of QCD
- Nucleon Compton scattering in the Dyson-Schwinger approach
- Exploring the Quark-Gluon Vertex with Slavnov-Taylor Identities and Lattice Simulations
- The Quark-Gluon Vertex and the QCD Infrared Dynamics
- The soft-gluon limit and the infrared enhancement of the quark-gluon vertex
- Underdetermined Dyson-Schwinger equations
- Forward sum rule for the -exchange correction to the charge radius extraction from elastic electron scattering
- Lattice QCD calculation of the two-photon exchange contribution to the muonic-hydrogen Lamb shift
- A fresh look at the (non-)Abelian Landau-Khalatnikov-Fradkin transformations
- First Determination of the 27Al Neutron Distribution Radius from a Parity-Violating Electron Scattering Measurement
- Measurement of deeply virtual Compton scattering off Helium-4 with CLAS at Jefferson Lab
- On Extraction of Twist-Two Compton Form Factors from DVCS Observables Through Harmonic Analysis
- Landau-Khalatnikov-Fradkin Transformations, Nielsen Identities, Their Equivalence and Implications for QCD
- Four-point Green functions in the Schwinger Model
- Lattice pure gauge compact QED in the Landau gauge: the photon propagator, the phase structure and the presence of Dirac strings
- The lattice Landau gauge photon propagator for 4D compact QED
- The Schwinger function, confinement and positivity violation in pure gauge QED
- Landau-Khalatnikov-Fradkin transformations for the two loop massless quark propagator
- Panel discussion: What {\it don't} we know about confinement?