271 research outputs found
The Infrared Behaviour of the Running Coupling in Landau Gauge QCD
Approximate solutions for the gluon and ghost propagators as well as the
running coupling in Landau gauge Yang-Mills theories are presented. These
propagators obtained from the corresponding Dyson-Schwinger equations are in
remarkable agreement with those of recent lattice calculations. The resulting
running coupling possesses an infrared fixed point,
for all gauge groups SU(). Above one GeV the running coupling rapidly
approaches its perturbative form.Comment: 8 pages, 3 figures, uses ActaStyle.cls, Invited talk given by R.A. at
the conference RENORMALIZATION GROUP 2002, March 10 - 16, 2002, Strba,
Slovaki
Kugo-Ojima confinement criterion, Zwanziger-Gribov horizon condition, and infrared critical exponents in Landau gauge QCD
The Kugo-Ojima confinement criterion and its relation to the infrared
behaviour of the gluon and ghost propagators in Landau gauge QCD are reviewed.
The realization of this confinement criterion (which in Landau gauge relates to
Zwanziger's horizon condition) results from quite general properties of the
ghost Dyson-Schwinger equation. The numerical solutions for the gluon and ghost
propagators obtained from a truncated set of Dyson-Schwinger equations provide
an explicit example for the anticipated infrared behaviour. These results are
in good agreement, also quantitatively, with corresponding lattice data
obtained recently. The resulting running coupling approaches a fixed point in
the infrared, . Solutions for the coupled system of
Dyson-Schwinger equations for the quark, gluon and ghost propagators are
presented. Dynamical generation of quark masses and thus spontaneous breaking
of chiral symmetry is found. In the quenched approximation the quark propagator
functions agree well with those of corresponding lattice calculations. For a
small number of light flavours the quark, gluon and ghost propagators deviate
only slightly from the quenched ones. While the positivity violation of the
gluon spectral function is apparent in the gluon propagator, there are no clear
indications of positivity violations in the Landau gauge quark propagator.Comment: 10 pages, 4 figures; invited talk presented by R. Alkofer at the
International Conference Confinement V Gargnano, Italy, September 10-14, 200
On dynamical gluon mass generation
The effective gluon propagator constructed with the pinch technique is
governed by a Schwinger-Dyson equation with special structure and gauge
properties, that can be deduced from the correspondence with the background
field method. Most importantly the non-perturbative gluon self-energy is
transverse order-by-order in the dressed loop expansion, and separately for
gluonic and ghost contributions, a property which allows for a meanigfull
truncation. A linearized version of the truncated Schwinger-Dyson equation is
derived, using a vertex that satisfies the required Ward identity and contains
massless poles. The resulting integral equation, subject to a properly
regularized constraint, is solved numerically, and the main features of the
solutions are briefly discussed.Comment: Special Article - QNP2006: 4th International Conference on Quarks and
Nuclear Physics, Madrid, Spain, 5-10 June 200
Infrared Exponents and the Running Coupling of Landau gauge QCD and their Relation to Confinement
The infrared behaviour of the gluon and ghost propagators in Landau gauge QCD
is reviewed. The Kugo-Ojima confinement criterion and the Gribov-Zwanziger
horizon condition result from quite general properties of the ghost
Dyson-Schwinger equation. The numerical solutions for the gluon and ghost
propagators obtained from a truncated set of Dyson-Schwinger equations provide
an explicit example for the anticipated infrared behaviour. The results are in
good agreement with corresponding lattice data obtained recently. The resulting
running coupling approaches a fix point in the infrared, . Two different fits for the scale dependence of the running coupling
are given and discussed.Comment: 3 pages, 3 figures; talk given by R.A. at the conference Quark
Nuclear Physics 200
Sarma phase in relativistic and non-relativistic systems
We investigate the stability of the Sarma phase in two-component fermion
systems in three spatial dimensions. For this purpose we compare
strongly-correlated systems with either relativistic or non-relativistic
dispersion relation: relativistic quarks and mesons at finite isospin density
and spin-imbalanced ultracold Fermi gases. Using a Functional Renormalization
Group approach, we resolve fluctuation effects onto the corresponding phase
diagrams beyond the mean-field approximation. We find that fluctuations induce
a second order phase transition at zero temperature, and thus a Sarma phase, in
the relativistic setup for large isospin chemical potential. This motivates the
investigation of the cold atoms setup with comparable mean-field phase
structure, where the Sarma phase could then be realized in experiment. However,
for the non-relativistic system we find the stability region of the Sarma phase
to be smaller than the one predicted from mean-field theory. It is limited to
the BEC side of the phase diagram, and the unitary Fermi gas does not support a
Sarma phase at zero temperature. Finally, we propose an ultracold quantum gas
with four fermion species that has a good chance to realize a zero-temperature
Sarma phase.Comment: version published in Phys.Lett.B; 10 pages, 5 figure
Verifying the Kugo-Ojima Confinement Criterion in Landau Gauge Yang-Mills Theory
Expanding the Landau gauge gluon and ghost two-point functions in a power
series we investigate their infrared behavior. The corresponding powers are
constrained through the ghost Dyson-Schwinger equation by exploiting
multiplicative renormalizability. Without recourse to any specific truncation
we demonstrate that the infrared powers of the gluon and ghost propagators are
uniquely related to each other. Constraints for these powers are derived, and
the resulting infrared enhancement of the ghost propagator signals that the
Kugo-Ojima confinement criterion is fulfilled in Landau gauge Yang-Mills
theory.Comment: 4 pages, no figures; version to be published in Physical Review
Letter
Propagators in Coulomb gauge from SU(2) lattice gauge theory
A thorough study of 4-dimensional SU(2) Yang-Mills theory in Coulomb gauge is
performed using large scale lattice simulations. The (equal-time) transverse
gluon propagator, the ghost form factor d(p) and the Coulomb potential V_{coul}
(p) ~ d^2(p) f(p)/p^2 are calculated. For large momenta p, the gluon propagator
decreases like 1/p^{1+\eta} with \eta =0.5(1). At low momentum, the propagator
is weakly momentum dependent. The small momentum behavior of the Coulomb
potential is consistent with linear confinement. We find that the inequality
\sigma_{coul} \ge \sigma comes close to be saturated. Finally, we provide
evidence that the ghost form factor d(p) and f(p) acquire IR singularities,
i.e., d(p) \propto 1/\sqrt{p} and f(p) \propto 1/p, respectively. It turns out
that the combination g_0^2 d_0(p) of the bare gauge coupling g_0 and the bare
ghost form factor d_0(p) is finite and therefore renormalization group
invariant.Comment: 10 pages, 7 figure
Infrared exponents and the strong-coupling limit in lattice Landau gauge
We study the gluon and ghost propagators of lattice Landau gauge in the
strong-coupling limit beta=0 in pure SU(2) lattice gauge theory to find
evidence of the conformal infrared behavior of these propagators as predicted
by a variety of functional continuum methods for asymptotically small momenta
. In the strong-coupling limit, this same
behavior is obtained for the larger values of a^2q^2 (in units of the lattice
spacing a), where it is otherwise swamped by the gauge field dynamics.
Deviations for a^2q^2 < 1 are well parameterized by a transverse gluon mass
. Perhaps unexpectedly, these deviations are thus no finite-volume
effect but persist in the infinite-volume limit. They furthermore depend on the
definition of gauge fields on the lattice, while the asymptotic conformal
behavior does not. We also comment on a misinterpretation of our results by
Cucchieri and Mendes in Phys. Rev. D81 (2010) 016005.Comment: 17 pages, 12 figures. Revised version (mainly sections I and II);
references and comments on subsequent work on the subject added
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