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Manuscript Title: Solving the gluon Dyson-Schwinger equation in the Mandelstam approximation.
Authors: A. Hauck, L. von Smekal, R. Alkofer
Program title: mandelstam
Catalogue identifier: ADII_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 112(1998)149
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 propagator, Landau gauge, Mandelstam approximation, Non-linear integral Equations, Infrared asymptotic Series, Constrained iterative Solution.
Classification: 11.5.

Nature of problem:
An approach to describing non-perturbative correlations in field theories is to investigate their Dyson-Schwinger equations in suitable truncation schemes. Thereby one generally encounters non-linear integral equations which in many cases have infrared singular solutions imposing stability problems in the numerical procedures.

Solution method:
The infrared singular part of the integral equation is studied analytically and transformed into constraints. Infrared subleading contributions are then obtained in form of an asymptotic series. This expansion of the solution can be calculated recursively and, together with the ultraviolet behaviour obtained from a differential equation, it makes a numerical solution tractable.

So far all contributions from Faddeev-Popov ghosts are neglected. An extended model based on analogous techniques is presented elsewhere [1,2].

Running time:
Approximately 10 sec.

[1] A. Hauck, L. von Smekal and R. Alkofer, Solving a Coupled Set of Truncated QCD Dyson-Schwinger Equations, Comp. Phys. Commun. 112 (1998) 166.
[2] 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.