15 research outputs found
Algorithmic derivation of Dyson-Schwinger Equations
We present an algorithm for the derivation of Dyson-Schwinger equations of
general theories that is suitable for an implementation within a symbolic
programming language. Moreover, we introduce the Mathematica package DoDSE
which provides such an implementation. It derives the Dyson-Schwinger equations
graphically once the interactions of the theory are specified. A few examples
for the application of both the algorithm and the DoDSE package are provided.
The package can be obtained from physik.uni-graz.at/~mah/DoDSE.html.Comment: 17 pages, 11 figures, downloadable Mathematica package v2: adapted to
version 1.2 of DoDSE package with simplified handling and improved plotting
of graphs; references adde
On the infrared scaling solution of SU(N) Yang-Mills theories in the maximally Abelian gauge
An improved method for extracting infrared exponents from functional
equations is presented. The generalizations introduced allow for an analysis of
quite complicated systems such as Yang-Mills theory in the maximally Abelian
gauge. Assuming the absence of cancellations in the appropriately renormalized
integrals the only consistent scaling solution yields an infrared enhanced
diagonal gluon propagator in support of the Abelian dominance hypothesis. This
is explicitly shown for SU(2) and subsequently verified for SU(N), where
additional interactions exist. We also derive the most infrared divergent
scaling solution possible for vertex functions in terms of the propagators'
infrared exponents. We provide general conditions for the existence of a
scaling solution for a given system and comment on the cases of linear
covariant gauges and ghost anti-ghost symmetric gauges.Comment: 23 pages, 10 figures; version coincides with version published in
EPJ
Infrared Behavior of Three-Point Functions in Landau Gauge Yang-Mills Theory
Analytic solutions for the three-gluon and ghost-gluon vertices in Landau
gauge Yang-Mills theory at low momenta are presented in terms of hypergeometric
series. They do not only show the expected scaling behavior but also additional
kinematic divergences when only one momentum goes to zero. These singularities,
which have also been proposed previously, induce a strong dependence on the
kinematics in many dressing functions. The results are generalized to two and
three dimensions and a range of values for the ghost propagator's infrared
exponent kappa.Comment: 21 pages, 29 figures; numerical data of the infrared dressing
functions can be obtained from the authors v2: a few minor changes,
corresponds to version appearing in EPJ
Strong-coupling study of the Gribov ambiguity in lattice Landau gauge
We study the strong-coupling limit beta=0 of lattice SU(2) Landau gauge
Yang-Mills theory. In this limit the lattice spacing is infinite, and thus all
momenta in physical units are infinitesimally small. Hence, the infrared
behavior can be assessed at sufficiently large lattice momenta. Our results
show that at the lattice volumes used here, the Gribov ambiguity has an
enormous effect on the ghost propagator in all dimensions. This underlines the
severity of the Gribov problem and calls for refined studies also at finite
beta. In turn, the gluon propagator only mildly depends on the Gribov
ambiguity.Comment: 14 pages, 22 figures; minor changes, matches version to appear in
Eur. Phys. J.
Truncating first-order Dyson-Schwinger equations in Coulomb-Gauge Yang-Mills theory
The non-perturbative domain of QCD contains confinement, chiral symmetry
breaking, and the bound state spectrum. For the calculation of the latter, the
Coulomb gauge is particularly well-suited. Access to these non-perturbative
properties should be possible by means of the Green's functions. However,
Coulomb gauge is also very involved, and thus hard to tackle. We introduce a
novel BRST-type operator r, and show that the left-hand side of Gauss' law is
r-exact.
We investigate a possible truncation scheme of the Dyson-Schwinger equations
in first-order formalism for the propagators based on an instantaneous
approximation. We demonstrate that this is insufficient to obtain solutions
with the expected property of a linear-rising Coulomb potential. We also show
systematically that a class of possible vertex dressings does not change this
result.Comment: 22 pages, 4 figures, 1 tabl
On the Nature of the Phase Transition in SU(N), Sp(2) and E(7) Yang-Mills theory
We study the nature of the confinement phase transition in d=3+1 dimensions
in various non-abelian gauge theories with the approach put forward in [1]. We
compute an order-parameter potential associated with the Polyakov loop from the
knowledge of full 2-point correlation functions. For SU(N) with N=3,...,12 and
Sp(2) we find a first-order phase transition in agreement with general
expectations. Moreover our study suggests that the phase transition in E(7)
Yang-Mills theory also is of first order. We find that it is weaker than for
SU(N). We show that this can be understood in terms of the eigenvalue
distribution of the order parameter potential close to the phase transition.Comment: 15 page
The Infrared Behaviour of the Pure Yang-Mills Green Functions
We review the infrared properties of the pure Yang-Mills correlators and
discuss recent results concerning the two classes of low-momentum solutions for
them reported in literature; i.e. decoupling and scaling solutions. We will
mainly focuss on the Landau gauge and pay special attention to the results
inferred from the analysis of the Dyson-Schwinger equations of the theory and
from "{\it quenched}" lattice QCD. The results obtained from properly
interplaying both approaches are strongly emphasized.Comment: Final version to be published in FBS (54 pgs., 11 figs., 4 tabs