70 research outputs found
Hamiltonian approach to Yang-Mills theory in Coulomb gauge
Recent results obtained within the Hamiltonian approach to continuum
Yang-Mills theory in Coulomb gauge are reviewed.Comment: 7 pages, 2 figures, to appear in the ``Quark Confinement and the
hadron spectrum VII'' (Portugal 2006) conference proceeding
Infrared analysis of propagators and vertices of Yang--Mills theory in Landau and Coulomb gauge
The infrared behaviour of gluon and ghost propagators, ghost-gluon vertex and
three-gluon vertex is investigated for both the covariant Landau and the
non-covariant Coulomb gauge. Assuming infrared ghost dominance, we find a
unique infrared exponent in the d=4 Landau gauge, while in the d=3+1 Coulomb
gauge we find two different infrared exponents. We also show that a finite
dressing of the ghost-gluon vertex has no influence on the infrared exponents.
Finally, we determine the infrared behaviour of the three-gluon vertex
analytically and calculate it numerically at the symmetric point in the Coulomb
gauge.Comment: 25 pages, 6 figures, accepted by Phys. Rev. D, references added,
typos correcte
Confining Solution of the Dyson-Schwinger Equations in Coulomb Gauge
The Dyson-Schwinger equations arising from minimizing the vacuum energy
density in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge are
solved numerically. A new solution is presented which gives rise to a strictly
linearly rising static quark potential and whose existence was previously
observed in the infrared analysis of the Dyson-Schwinger equations. For the new
solution we also present the static quark potential and calculate the running
coupling constant from the ghost-gluon vertex.Comment: 9 pages, 3 figures, references added
Exploratory study of three-point Green's functions in Landau-gauge Yang-Mills theory
Green's functions are a central element in the attempt to understand
non-perturbative phenomena in Yang-Mills theory. Besides the propagators,
3-point Green's functions play a significant role, since they permit access to
the running coupling constant and are an important input in functional methods.
Here we present numerical results for the two non-vanishing 3-point Green's
functions in 3d pure SU(2) Yang-Mills theory in (minimal) Landau gauge, i.e.
the three-gluon vertex and the ghost-gluon vertex, considering various
kinematical regimes. In this exploratory investigation the lattice volumes are
limited to 20^3 and 30^3 at beta=4.2 and beta=6.0. We also present results for
the gluon and the ghost propagators, as well as for the eigenvalue spectrum of
the Faddeev-Popov operator. Finally, we compare two different numerical methods
for the evaluation of the inverse of the Faddeev-Popov matrix, the point-source
and the plane-wave-source methods.Comment: 18 pages, 12 figures, 3 table
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