Solving a Coupled Set of Truncated QCD Dyson-Schwinger Equations

Truncated Dyson-Schwinger equations represent finite subsets of the equations of motion for Green's functions. Solutions to these non-linear integral equations can account for non-perturbative correlations. A closed set of coupled Dyson-Schwinger equations for the propagators of gluons and ghosts in Landau gauge QCD is obtained by neglecting all contributions from irreducible 4-point correlations and by implementing the Slavnov-Taylor identities for the 3-point vertex functions. We solve this coupled set in an one-dimensional approximation which allows for an analytic infrared expansion necessary to obtain numerically stable results. This technique, which was also used in our previous solution of the gluon Dyson-Schwinger equation in the Mandelstam approximation, is here extended to solve the coupled set of integral equations for the propagators of gluons and ghosts simultaneously. In particular, the gluon propagator is shown to vanish for small spacelike momenta whereas the previoulsy neglected ghost propagator is found to be enhanced in the infrared. The running coupling of the non-perturbative subtraction scheme approaches an infrared stable fixed point at a critical value of the coupling, alpha_c approximately 9.5.Comment: 23 pages, 6 figures, LaTeX2

INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND GENERAL

We consider the double mathematical pendulum in the limit when the ratio of pendulum masses is close to zero and the ratio of pendulum lengths is close to infinity. We found that the limit system has a hyperbolic periodic trajectory, whose invariant manifolds intersect transversally and the intersections are exponentially small. In this case we obtain an asymptotic formula of the homoclinic invariant for the limit system. PACS numbers: 45.20Jj, 02.30.Hq, 05.45.-a 1