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Manuscript Title: Solving a coupled set of truncated QCD Dyson-Schwinger equations.
Authors: A. Hauck, L. von Smekal, R. Alkofer
Program title: gluonghost
Catalogue identifier: ADIH_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 112(1998)166
Programming language: Fortran.
Computer: DEC Alpha 500.
Operating system: UNIX.
RAM: 200K words
Word size: 32
Peripherals: disc.
Keywords: Particle physics, Elementary, Qcd, Non-perturbative qcd, Dyson-schwinger Equations, Gluon and ghost Propagator, Landau gauge, Mandelstam approximation, Non-linear integral Equations, Infrared asymptotic Series, Constrained iterative Solution.
Classification: 11.5.

Nature of problem:
One non-perturbative approach to non-Abelian gauge theories is to investigate their Dyson-Schwinger equations in suitable truncation schemes. For the pure gauge theory, i.e., for gluons and ghosts in Landau gauge QCD without quarks, such a scheme is derived in Ref. [1]. In numerical solutions one generally encounters non-linear, infrared singular sets of coupled integral equations.

Solution method:
The singular part of the integral equations is treated analytically and transformed into constraints extending our previous work [2] to a coupled system of equations. The solution in the infrared is then expanded into an asymptotic series which together with the known ultraviolet behaviour makes a numerical solution tractable.

Solving the coupled system of Dyson-Schwinger equations relies on a modified angle approximation to reduce the 4-dimensional integrals to one-dimensional ones.

Running time:
One minute.

[1] L. von Smekal, A. Hauck and R. Alkofer, Phys. Rev. Lett. 79 (1997), 3591: L. von Smekal, A. Hauck and R. Alkofer, A Solution to Coupled Dyson-Schwinger Equations for Gluons and Ghosts in Landau Gauge, hep-ph 9707327, e-print, submitted to Ann. Phys., and references therein.
[2] A. Hauck, L. von Smekal and R. Alkofer, Solving the Gluon Dyson- Schwinger Equation in the Mandelstam Approximation, Comp. Phys. Commun. 112 (1998) 149.