39,956 research outputs found
Dyson-Schwinger Equations and Coulomb Gauge Yang-Mills Theory
Coulomb gauge Yang-Mills theory is considered within the first order
formalism. It is shown that the action is invariant under both the standard BRS
transform and an additional component. The Ward-Takahashi identity arising from
this non-standard transform is shown to be automatically satisfied by the
equations of motion.Comment: 3 pages, talk given at Quark Confinement and the Hadron Spectrum VII
(2-7 Sep, 2006), Ponta Delgada, Azore
The ghost propagator in Coulomb gauge
We present results for a numerical study of the ghost propagator in Coulomb
gauge whereby lattice results for the spatial gluon propagator are used as
input to solving the ghost Dyson-Schwinger equation. We show that in order to
solve completely, the ghost equation must be supplemented by a boundary
condition (the value of the inverse ghost propagator dressing function at zero
momentum) which determines if the solution is critical (zero value for the
boundary condition) or subcritical (finite value). The various solutions
exhibit a characteristic behavior where all curves follow the same (critical)
solution when going from high to low momenta until `forced' to freeze out in
the infrared to the value of the boundary condition. The boundary condition can
be interpreted in terms of the Gribov gauge-fixing ambiguity; we also
demonstrate that this is not connected to the renormalization. Further, the
connection to the temporal gluon propagator and the infrared slavery picture of
confinement is discussed.Comment: 3 pages, 2 figures, talk presented at "Quark Confinement and the
Hadron Spectrum IX", Madrid, August 30-September 3, 2010, to appear in the
proceeding
Coulomb gauge confinement in the heavy quark limit
The relationship between the nonperturbative Green's functions of Yang-Mills
theory and the confinement potential is investigated. By rewriting the
generating functional of quantum chromodynamics in terms of a heavy quark mass
expansion in Coulomb gauge, restricting to leading order in this expansion and
considering only the two-point functions of the Yang-Mills sector, the
rainbow-ladder approximation to the gap and Bethe-Salpeter equations is shown
to be exact in this case and an analytic, nonperturbative solution is
presented. It is found that there is a direct connection between the string
tension and the temporal gluon propagator. Further, it is shown that for the
4-point quark correlation functions, only confined bound states of
color-singlet quark-antiquark (meson) and quark-quark (baryon) pairs exist.Comment: 22 pages, 6 figure
A Bethe--Salpeter Description of Light Mesons
We present a covariant approach to describe the low--lying scalar,
pseudoscalar, vector and axialvector mesons as quark--antiquark bound
states.This approach is based on an effective interaction modeling of the
non--perturbative structure of the gluon propagator that enters the quark
Schwinger--Dyson and meson Bethe--Salpeter equations. We extract the meson
masses and compute the pion and kaon decay constants. We obtain a
quantitatively correct description for pions, kaons and vector mesons while the
calculated spectra of scalar and axialvector mesons suggest that their
structure is more complex than being quark--antiquark bound states.Comment: Talk presented by HW at the international Scalar Meson Workshop,
Utica, NY, May 2003; 12 pages, uses aip style file
Leading order infrared quantum chromodynamics in Coulomb gauge
A truncation scheme for the Dyson-Schwinger equations of quantum
chromodynamics in Coulomb gauge within the first order formalism is presented.
The truncation is based on an Ansatz for the Coulomb kernel occurring in the
action. Results at leading loop order and in the infrared are discussed for
both the Yang-Mills and quark sectors. It is found that the resulting equations
for the static gluon and quark propagators agree with those derived in a
quasi-particle approximation to the canonical Hamiltonian approach. Moreover, a
connection to the heavy quark limit is established. The equations are analyzed
numerically and it is seen that in both the gluonic and quark sectors, a
nontrivial dynamical infrared mass scale emerges.Comment: 27 pages, 11 figure
Perturbation Theory of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism
Perturbative Coulomb gauge Yang-Mills theory within the first order formalism
is considered. Using a differential equation technique and dimensional
regularization, analytic results for both the ultraviolet divergent and finite
parts of the two-point functions at one-loop order are derived. It is shown how
the non-ultraviolet divergent parts of the results are finite at spacelike
momenta with kinematical singularities on the light-cone and subsequent branch
cuts extending into the timelike region.Comment: 23 pages, 6 figure
Quark-gluon vertex dressing and meson masses beyond ladder-rainbow truncation
We include a generalized infinite class of quark-gluon vertex dressing
diagrams in a study of how dynamics beyond the ladder-rainbow truncation
influences the Bethe-Salpeter description of light quark pseudoscalar and
vector mesons. The diagrammatic specification of the vertex is mapped into a
corresponding specification of the Bethe-Salpeter kernel, which preserves
chiral symmetry. This study adopts the algebraic format afforded by the simple
interaction kernel used in previous work on this topic. The new feature of the
present work is that in every diagram summed for the vertex and the
corresponding Bethe-Salpeter kernel, each quark-gluon vertex is required to be
the self-consistent vertex solution. We also adopt from previous work the
effective accounting for the role of the explicitly non-Abelian three gluon
coupling in a global manner through one parameter determined from recent
lattice-QCD data for the vertex. With the more consistent vertex used here, the
error in ladder-rainbow truncation for vector mesons is never more than 10% as
the current quark mass is varied from the u/d region to the b region.Comment: 15 pages, 12 figure
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