Nonperturbative Approaches to Determining the Behavior of the Gluon Propagator and Quark Propagator in Quantum Chromodynamics by Schwinger-Dyson Equations

Hädicke, A.

doi:10.1142/s0217751x91001611

Cited by 14 publications

(15 citation statements)

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“…[See also, Hädicke (1991).] This is important because in the application of DSEs to hadronic physics a physically reasonable form for the quark propagator is needed and, in practice, this is obtained by solving the quark DSE with Ansätze for the gluon propagator and quark-gluon vertex, with the former often being motivated by studies of the DSE for the gluon propagator.…”

Section: Gauge Boson Sector Of Qcdmentioning

confidence: 99%

“…The pragmatic benefit of Eq. (6.43) is again obvious: we are confronted with differential equations instead of integral equations [e.g., Roberts and McKellar (1990), Haeri andHaeri (1991), Williams et al (1991), Hawes and Williams (1991), Hädicke (1991)]. Hence we can obtain solutions for both spacelike and timelike momenta, which enables a study of the singularity structure of the quark propagator.…”

Section: Quark Confinementmentioning

confidence: 99%

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Dyson-Schwinger equations and their application to hadronic physics

Roberts¹,

Williams

1995

185

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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. KEYWORDS confinement of quarks and gluons; dynamical chiral symmetry breaking; Dyson-Schwinger equations; hadrons; quantum electrodynamics; quantum chromodynamics.

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Section: Gauge Boson Sector Of Qcdmentioning

confidence: 99%

Section: Quark Confinementmentioning

confidence: 99%

Dyson-Schwinger equations and their application to hadronic physics

Roberts¹,

Williams

1995

185

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“…This manifestly relativistically covariant approach, recent reviews of which can be found in Refs. [2,3], has provided the foundation for a useful and successful understanding of the phenomena of low-energy QCD by facilitating the construction of realistic field-theoretic models [4].…”

Section: Introductionmentioning

confidence: 99%

Dynamical chiral symmetry breaking and confinement with an infrared-vanishing gluon propagator?

1994

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We study a model Dyson-Schwinger equation for the quark propagator closed using an Ansatz for the gluon propagator of the form D(q) -q2/[(q2)' + b4] and two Ansatze for the quark-gluon vertex: the minimal Ball-Chiu form and the modified form suggested by Curtis and Pennington. Using the quark condensate as an order parameter, we find that there is a critical value of b = b, such that the model does not support dynamical chiral symmetry breaking for b > b,. We discuss and apply a confinement test which suggests that, for all values of b, the quark propagator in the model is not confining. Together these results suggest that this Ansatz for the gluon propagator is inadequate as a model since it does not yield the expected behavior of QCD.

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“…we consider eq. (10) with the model kernel of the form (13). The parameters of the model are presented in Table I.…”

Section: Numerical Results For Iteration Methodsmentioning

confidence: 99%

The Spectrum and Confinement for the Bethe-Salpeter Equation

Umnikov

Khanna

1996

Int. J. Mod. Phys. A

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The problem of calculating the mass spectrum of the two-body Bethe-Salpeter equation is studied with no reduction to the three-dimensional (“quasipotential”) equation. The method to find the ground state and excited states for a channel with any quantum numbers is presented. The problem of the confining interaction for the Bethe-Salpeter equation is discussed from the point of view of formal properties of the bound state spectrum, but with only inspiration from QCD. We study the kernel that is nonvanishing at large Euclidean intervals, i.e. RE→∞, which is constructed as a special limiting case of the sum of the covariant one-boson-exchange kernels. In the coordinate space this kernel is just a positive constant and corresponds to the kernel ∝ δ(kE) in the momentum space. When the usual attractive interaction is added, it is found that this kernel is similar in its effect to the nonrelativistic potential in coordinate space, V(r), with V(r→∞)→V∞. The positive real constant V∞ gives the scale that defines the limit of the bound state spectrum compared to the sum of the constituent masses, M < 2m+V∞. At the same time, the self-energy corrections remove the singularities from the propagators of the constituents, i.e. constituents do not propagate as free particles. The combination of these features of the solutions allows an interpretation of this type of interaction as a confining one. The illustrative analytical and numerical calculations are presented for a model of massive scalar particles with scalar interaction, i.e. the “massive Wick model.”

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Nonperturbative Approaches to Determining the Behavior of the Gluon Propagator and Quark Propagator in Quantum Chromodynamics by Schwinger-Dyson Equations

Cited by 14 publications

References 0 publications

Dyson-Schwinger equations and their application to hadronic physics

Dyson-Schwinger equations and their application to hadronic physics

Dynamical chiral symmetry breaking and confinement with an infrared-vanishing gluon propagator?

The Spectrum and Confinement for the Bethe-Salpeter Equation

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