Non-perturbative constraints on the quark and ghost propagators

Abstract

In QCD both the quark and ghost propagators are important for governing the non-perturbative dynamics of the theory. It turns out that the dynamical properties of the quark and ghost fields impose non-perturbative constraints on the analytic structure of these propagators. In this work we explicitly derive these constraints. In doing so we establish that the corresponding spectral densities include components which are multiples of discrete mass terms, and that the propagators are permitted to contain singular contributions involving derivatives of $\delta (p)$, both of which are particularly relevant in the context of confinement.

13 pages; v3: matches published version

References in corpus (6)

• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• Quark Confinement: The Hard Problem of Hadron Physics
• The non-perturbative structure of the photon and gluon propagators
• Conditions on the violation of the cluster decomposition property in QCD
• Infrared Gluon and Ghost Propagator Exponents From Lattice QCD
• Spectral density constraints in quantum field theory

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• Reconstructing confined particles with complex singularities
• Complex poles and spectral functions of Landau gauge QCD and QCD-like theories
• Non-perturbative strong coupling at timelike momenta
• Some remarks on the spectral functions of the Abelian Higgs Model
• Probing the singularities of the Landau-gauge gluon and ghost propagators with rational approximants
• On the complex structure of Yang-Mills theory
• Continuum approach to real time dynamics of 1+1D gauge field theory: out of horizon correlations of the Schwinger model
• Effective locality and chiral symmetry breaking in QCD
• Effects of a quark chemical potential on the analytic structure of the gluon propagator
• Extracting topological information from momentum space propagators
• Non-perturbative BRST symmetry and the spectral structure of the ghost propagator
• Reconstructing propagators of confined particles in the presence of complex singularities