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Dyson-Schwinger Equations and the Application to Hadronic Physics

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arxiv hep-ph/9403224 v2 pith:O46RRZC5 submitted 1994-03-03 hep-ph nucl-th

C. D. Roberts , A. G. Williams This is my paper · ORCID
classification hep-phnucl-th
keywords applicationgaugestrongcurrentdyson-schwingerformalismhadronicphysics
verification ladder T0 review T1 audit T2 compute T3 formal

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We review the current status of nonperturbative studies of gauge field theory using the Dyson-Schwinger equation formalism and its application to hadronic physics. We begin with an introduction to the formalism and a discussion of renormalisation in this approach. We then review the current status of studies of Abelian gauge theories [e.g., strong coupling quantum electrodynamics] before turning our attention to the non-Abelian gauge theory of the strong interaction, quantum chromodynamics. We discuss confinement, dynamical chiral symmetry breaking and the application and contribution of these techniques to our understanding of the strong interactions.

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Cited by 13 Pith papers

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  2. Bootstrapping Yang-Mills matrix integrals

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    Bootstrap bounds on ⟨tr XX⟩ and ⟨tr XXXX⟩ in D-matrix Yang-Mills integrals shrink to islands matching Monte Carlo, with large-D trajectories guiding a positivity-free ansatz.

  3. FunKit: A computer algebra toolkit for functional approaches

    hep-ph 2026-05 unverdicted novelty 6.0 of 10

    FunKit is a computer algebra toolkit that automates derivation of functional equations such as Dyson-Schwinger and functional RG from arbitrary master equations, with tracing via FORM and export to numerical code.

  4. Lee Yang edge singularities of QCD in association with Roberge-Weiss phase transition and chiral phase transition

    hep-ph 2025-04 conditional novelty 6.0 of 10

    Including a confining background field in Dyson-Schwinger equations makes Lee-Yang edge singularities terminate at the Roberge-Weiss line, mu_i = pi T / 3, above T = 0.235 GeV, while leaving the critical exponent unchanged.

  5. Insights into the $\mathbf{\gamma^{(*)} + N(940)\frac{1}{2}^+ \to \Delta(1700)\frac{3}{2}^{-}}$ transition

    hep-ph 2025-02 accept novelty 6.0 of 10

    First SCI-DSE quark-diquark calculation of the gamma* N -> Delta(1700) transition form factors and helicity amplitudes, benchmarked against JLab and CLAS data.

  6. Distribution amplitudes of heavy-light pseudo-scalar and vector mesons from Dyson-Schwinger equations framework

    hep-ph 2025-01 conditional novelty 6.0 of 10

    First DSE predictions for B*, B*_s, and B*_c distribution amplitudes show peaks near the Euclidean constituent quark mass ratio and a universal spin ordering.

  7. Exact Lattice Identities and Continuum-Limit Dyson--Schwinger Equations for Yang-Mills Theory

    hep-th 2026-08 reject novelty 5.0 of 10

    Using Haar-measure invariance on the lattice, the authors derive continuum Dyson-Schwinger equations for Yang-Mills and reduce them to a scalar system, but a sign error in the color algebra invalidates the scalar closure.

  8. A Critical Point on the Hairy Black Hole Phase Boundary in the Improved Holographic Einstein-Maxwell-Dilaton Theory

    hep-th 2025-09 conditional novelty 5.0 of 10

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    Using a maximum-entropy inversion of DSE/BSE form factors, the authors map meson charge profiles and find quark-antiquark distances that shrink with quark mass and grow by 5-15% for spin-aligned mesons.

  10. Anisotropic quark propagation and Zeeman effect in an external magnetic field

    hep-ph 2025-04 conditional novelty 5.0 of 10

    A Dyson-Schwinger calculation shows that in a magnetic field, quarks acquire distinct transverse and longitudinal effective masses, with the transverse mass always larger, and a mass splitting that grows roughly as th...

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    hep-ph 2024-11 conditional novelty 5.0 of 10

    A Dyson-Schwinger/Bethe-Salpeter calculation predicts g_D*Dpi = 16.22 and g_B*Bpi = 40.09, with static couplings consistent with lattice results.

  12. Electroexcitation of Nucleon Resonances and the Emergence of Hadron Mass

    hep-ph 2025-05 conditional novelty 2.0 of 10

    A review argues that Jefferson Lab electroproduction data on nucleon resonances, analyzed with continuum Schwinger methods, confirm a momentum-dependent dressed quark mass, the essence of emergent hadron mass.

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    A comprehensive review showing how massless composite poles in QCD vertices can generate the gluon mass scale, with a BSE-based computation reaching m=367 MeV against the 354 MeV lattice value.

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