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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_0Distribution 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. | ||

Restrictions: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. | ||

References: | ||

[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. |

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