196 research outputs found
Spurious divergences in Dyson-Schwinger equations
We revisit the treatment of spurious ultraviolet divergences in the equation
of motion of the gluon propagator caused by a momentum cutoff and the resulting
violation of gauge invariance. With present continuum studies of the gluon
propagator from its Dyson-Schwinger equation reaching the level of
quantitatively accurate descriptions, it becomes increasingly important to
understand how to subtract these spurious divergences in an unambiguous way.
Here we propose such a method. It is based entirely on the asymptotic
perturbative behavior of the QCD Green's functions without affecting
non-perturbative aspects such as mass terms or the asymptotic infrared
behavior. As a particular example, this allows us to assess the possible
influence of the tadpole diagram beyond perturbation theory. Finally, we test
this method numerically by solving the system of Dyson-Schwinger equations of
the gluon and ghost propagators.Comment: 19 pages, 9 figs; agrees with published versio
Going beyond the propagators of Landau gauge Yang-Mills theory
We present results for the propagators and the ghost-gluon vertex of Landau
gauge Yang-Mills theory obtained from Dyson-Schwinger equations. Solving these
three quantities simultaneously constitutes a new step in truncating these
equations. We also introduce a new model for the three-gluon vertex that is
motivated by lattice results. It features a zero crossing which is confirmed a
posteriori by a Dyson-Schwinger calculation. Within our setup we can reproduce
lattice data very well. We establish that also for the ghost-gluon vertex a
difference between decoupling and scaling solutions is present. For the scaling
solution we discuss the possibility of modifying the infrared exponents via an
angle dependence of the ghost-gluon vertex. However, no such dependence is
found in our calculations. Finally, we calculate the Schwinger function for the
gluon propagator.Comment: 8 pages, Confinement X proceeding
On the influence of three-point functions on the propagators of Landau gauge Yang-Mills theory
We solve the Dyson-Schwinger equations of the ghost and gluon propagators of
Landau gauge Yang-Mills theory together with that of the ghost-gluon vertex.
The latter plays a central role in many truncation schemes for functional
equations. By including it dynamically we can determine its influence on the
propagators. We also suggest a new model for the three-gluon vertex motivated
by lattice data which plays a crucial role to obtain stable solutions when the
ghost-gluon vertex is included. We find that both vertices have a sizable
quantitative impact on the mid-momentum regime and contribute to the reduction
of the gap between lattice and Dyson-Schwinger equation results. Furthermore,
we establish that the three-gluon vertex dressing turns negative at low momenta
as suggested by lattice results in three dimensions.Comment: 28 pages, 12 figures, matches published versio
Infrared scaling solutions beyond the Landau gauge: The maximally Abelian gauge and Abelian infrared dominance
Functional equations like exact renormalization group and Dyson-Schwinger
equations have contributed to a better understanding of non-perturbative
phenomena in quantum field theories in terms of the underlying Green functions.
In Yang-Mills theory especially the Landau gauge has been used, as it is the
most accessible gauge for these methods. The growing understanding obtained in
this gauge allows to proceed to other gauges in order to obtain more
information about the relation of different realizations of the confinement
mechanism. In the maximally Abelian gauge first results are very encouraging as
a variant of Abelian infrared dominance is found: The Abelian part of the gauge
field propagator is enhanced at low momenta and thereby dominates the dynamics
in the infrared. Its role is therefore similar to that of the ghost propagator
in the Landau gauge, where one denotes the corresponding phenomenon as ghost
dominance. Also the ambiguity of two different types of solutions (decoupling
and scaling) exists in both gauges. Here we present how the two solutions are
related in the maximally Abelian gauge. The intricacy of the system of
functional equations in this gauge required the development of some new tools
and methods as, for example, the automated derivation of the equations by the
program DoFun. We also present results for linear covariant and ghost
anti-ghost symmetric gauges.Comment: 10 pages, 2 figures, Proceedings of The Many faces of QCD, Nov. 1-5
2010, Ghent, Belgiu
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