993,263 research outputs found
Null structure and local well-posedness in the energy class for the Yang-Mills equations in Lorenz gauge
We demonstrate null structure in the Yang-Mills equations in Lorenz gauge.
Such structure was found in Coulomb gauge by Klainerman and Machedon, who used
it to prove global well-posedness for finite-energy data. Compared with Coulomb
gauge, Lorenz gauge has the advantage---shared with the temporal gauge---that
it can be imposed globally in space even for large solutions. Using the null
structure and bilinear space-time estimates, we also prove local-in-time
well-posedness of the equations in Lorenz gauge, for data with finite energy.
The time of existence depends on the initial energy and on the -norm of the initial potential, for some .Comment: Minor typos corrected, references update
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
What can we learn about Gribov copies from a formulation of QCD in terms of gauge-invariant fields?
We review the procedure by which we implemented the non-Abelian Gauss's law
and constructed gauge-invariant fields for QCD in the temporal (Weyl) gauge. We
point out that the operator-valued transformation that transforms
gauge-dependent temporal-gauge fields into gauge-invariant ones has the formal
structure of a gauge transformation. We express the ``standard'' Hamiltonian
for temporal-gauge QCD entirely in terms of gauge-invariant fields, calculate
the commutation rules for these fields, and compare them to earlier work on
Coulomb-gauge QCD. We also discuss multiplicities of gauge-invariant
temporal-gauge fields that belong to different topological sectors and that, in
previous work, were shown to be based on the same underlying gauge-dependent
temporal-gauge fields. We relate these multiplicities of gauge-invariant fields
to Gribov copies. We argue that Gribov copies appear in the temporal gauge, but
not when the theory is represented in terms of gauge-dependent fields and
Gauss's law is left unimplemented. There are Gribov copies of the
gauge-invariant gauge field, which can be constructed when Gauss's law is
implemented.Comment: To appear in Proceedings of the 6th Workshop on Non-Perturbative QCD,
Paris, France, June 5-9, 200
General Gauge Mediation with Gauge Messengers
We generalize the General Gauge Mediation formalism to allow for the
possibility of gauge messengers. Gauge messengers occur when charged matter
fields of the susy-breaking sector have non-zero F-terms, which leads to
tree-level, susy-breaking mass splittings in the gauge fields. A classic
example is that SU(5) / SU(3) x SU(2) x U(1) gauge fields could be gauge
messengers. We give a completely general, model independent, current-algebra
based analysis of gauge messenger mediation of susy-breaking to the visible
sector. Characteristic aspects of gauge messengers include enhanced
contributions to gaugino masses, (tachyonic) sfermion mass-squareds generated
already at one loop, and also at two loops, and significant one-loop A-terms,
already at the messenger scale.Comment: 79 pages, 5 figure
Gauge dependence in topological gauge theories
We parametrize the gauge-fixing freedom in choosing the Lagrangian of a
topological gauge theory. We compute the gauge-fixing dependence of correlators
of equivariant operators when the compactified moduli space has a non-empty
boundary and verify that only a subset of these has a gauge independent
meaning. We analyze in detail a simple example of such anomalous topological
theories, 4D topological Yang-Mills on the four-sphere and instanton number
k=1.Comment: 12 pages, TeX , harvma
Gauge-invariant quark and gluon fields in QCD: dynamics, topology, and the Gribov ambiguity
We review the implementation, in a temporal-gauge formulation of QCD, of the
non-Abelian Gauss's law and the construction of gauge-invariant gauge and
matter fields. We then express the QCD Hamiltonian in terms of these
gauge-invariant operator-valued fields, and discuss the relation of this
Hamiltonian and the gauge-invariant fields to the corresponding quantities in a
Coulomb gauge formulation of QCD. We argue that a representation of QCD in
terms of gauge-invariant quantities could be particularly useful for
understanding low-energy phenomenology. We present the results of an
investigation into the topological properties of the gauge-invariant fields,
and show that there are Gribov copies of these gauge-invariant gauge fields,
which are constructed in the temporal gauge, even though the conditions that
give rise to Gribov copies do not obtain for the gauge-dependent temporal-gauge
fields.Comment: 5 pages LaTex; talk presented at light-cone workshop "Particles and
Strings", Trento, Italy, September 200
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