28 research outputs found
A study of the Gribov copies in linear covariant gauges in Euclidean Yang-Mills theories
The Gribov copies and their consequences on the infrared behavior of the
gluon propagator are investigated in Euclidean Yang-Mills theories quantized in
linear covariant gauges. Considering small values of the gauge parameter, it
turns out that the transverse component of the gluon propagator is suppressed,
while its longitudinal part is left unchanged. A Green function, G_{tr}, which
displays infrared enhancement and which reduces to the ghost propagator in the
Landau gauge is identified. The inclusion of the dimension two gluon condensate
is also considered. In this case, the transverse component of the gluon
propagator and the Green function G_{tr} remain suppressed and enhanced,
respectively. Moreover, the longitudinal part of the gluon propagator becomes
suppressed. A comparison with the results obtained from the studies of the
Schwinger-Dyson equations and from lattice simulations is provided.Comment: 20 page
A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
Recent lattice data have reported an infrared suppressed, positivity
violating gluon propagator which is nonvanishing at zero momentum and a ghost
propagator which is no longer enhanced. This paper discusses how to obtain
analytical results which are in qualitative agreement with these lattice data
within the Gribov-Zwanziger framework. This framework allows one to take into
account effects related to the existence of gauge copies, by restricting the
domain of integration in the path integral to the Gribov region. We elaborate
to great extent on a previous short paper by presenting additional results,
also confirmed by the numerical simulations. A detailed discussion on the soft
breaking of the BRST symmetry arising in the Gribov-Zwanziger approach is
provided.Comment: 38 pages, 9 figures, the content of section V has been extended and
adapte
A study of the gauge invariant, nonlocal mass operator in Yang-Mills theories
The nonlocal mass operator is
considered in Yang-Mills theories in Euclidean space-time. It is shown that the
operator can be cast in local
form through the introduction of a set of additional fields. A local and
polynomial action is thus identified. Its multiplicative renormalizability is
proven by means of the algebraic renormalization in the class of linear
covariant gauges. The anomalous dimensions of the fields and of the mass
operator are computed at one loop order. A few remarks on the possible role of
this operator for the issue of the gauge invariance of the dimension two
condensates are outlined.Comment: 34 page
Hamiltonian structures of fermionic two-dimensional Toda lattice hierarchies
By exhibiting the corresponding Lax pair representations we propose a wide
class of integrable two-dimensional (2D) fermionic Toda lattice (TL)
hierarchies which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL
hierarchies as particular cases. We develop the generalized graded R-matrix
formalism using the generalized graded bracket on the space of graded operators
with involution generalizing the graded commutator in superalgebras, which
allows one to describe these hierarchies in the framework of the Hamiltonian
formalism and construct their first two Hamiltonian structures. The first
Hamiltonian structure is obtained for both bosonic and fermionic Lax operators
while the second Hamiltonian structure is established for bosonic Lax operators
only.Comment: 12 pages, LaTeX, the talks delivered at the International Workshop on
Classical and Quantum Integrable Systems (Dubna, January 24 - 28, 2005) and
International Conference on Theoretical Physics (Moscow, April 11 - 16, 2005
A study of the zero modes of the Faddeev-Popov operator in Euclidean Yang-Mills theories in the Landau gauge in d=2,3,4 dimensions
Examples of normalizable zero modes of the Faddeev-Popov operator in SU(2)
Euclidean Yang-Mills theories in the Landau gauge are constructed in d=2,3,4
dimensions.Comment: 18 pages. Text modifications. References added. Version accepted for
publication in the EPJ
Dynamical gluon mass generation from <A^2> in linear covariant gauges
We construct the multiplicatively renormalizable effective potential for the
mass dimension two local composite operator A^2 in linear covariant gauges. We
show that the formation of is energetically favoured and that the gluons
acquire a dynamical mass due to this gluon condensate. We also discuss the
gauge parameter independence of the resultant vacuum energy.Comment: 21 pages. 14 .eps figures. v2: minor modifications. v3: version
accepted for publication in JHE
Landau gauge within the Gribov horizon
We consider a model which effectively restricts the functional integral of
Yang--Mills theories to the fundamental modular region. Using algebraic
arguments, we prove that this theory has the same divergences as ordinary Yang
Mills theory in the Landau gauge and that it is unitary. The restriction of the
functional integral is interpreted as a kind of spontaneous breakdown of the
symmetry.Comment: 17 pages, NYU-TH-93/10/0
A Lattice Study of the Gluon Propagator in Momentum Space
We consider pure glue QCD at beta=5.7, beta=6.0 and beta=6.3. We evaluate the
gluon propagator both in time at zero 3-momentum and in momentum space. From
the former quantity we obtain evidence for a dynamically generated effective
mass, which at beta=6.0 and beta=6.3 increases with the time separation of the
sources, in agreement with earlier results. The momentum space propagator G(k)
provides further evidence for mass generation. In particular, at beta=6.0, for
k less than 1 GeV, the propagator G(k) can be fit to a continuum formula
proposed by Gribov and others, which contains a mass scale b, presumably
related to the hadronization mass scale. For higher momenta Gribov's model no
longer provides a good fit, as G(k) tends rather to follow an inverse power
law. The results at beta=6.3 are consistent with those at beta=6.0, but only
the high momentum region is accessible on this lattice. We find b in the range
of three to four hundred MeV and the exponent of the inverse power law about
2.7. On the other hand, at beta=5.7 (where we can only study momenta up to 1
GeV) G(k) is best fit to a simple massive boson propagator with mass m. We
argue that such a discrepancy may be related to a lack of scaling for low
momenta at beta=5.7. {}From our results, the study of correlation functions in
momentum space looks promising, especially because the data points in Fourier
space turn out to be much less correlated than in real space.Comment: 19 pages + 12 uuencoded PostScript picture
Equivariant Gauge Fixing of SU(2) Lattice Gauge Theory
I construct a Lattice Gauge Theory (LGT) with discrete Z_2 structure group
and an equivariant BRST symmetry that is physically equivalent to the standard
SU(2)-LGT. The measure of this Z_2-LGT is invariant under all the discrete
symmetries of the lattice and its partition function does not vanish. The
Topological Lattice Theories (TLT) that localize on the moduli spaces are
explicitly constructed and their BRST symmetry is exhibited. The ghosts of the
Z_2-invariant local LGT are integrated in favor of a nonlocal bosonic measure.
In addition to the SU(2) link variables and the coupling g^2, this effective
bosonic measure also depends on an auxiliary gauge invariant site variable of
canonical dimension two and on a gauge parameter \alpha. The relation between
the expectation value of the auxiliary field, the gauge parameter \alpha and
the lattice spacing is obtained to lowest order in the loop expansion. In
four dimensions and the critical limit this expectation value is a physical
scale proportional to \Lambda_L in the gauge \alpha=g^2 (11-n_f)/24+ O(g^4).
Implications for the loop expansion of observables in such a critical gauge are
discussed.Comment: 46 pages, Latex, updated and shortened version to appear in
Phys.Rev.
Landscape science: a Russian geographical tradition
The Russian geographical tradition of landscape science (landshaftovedenie) is analyzed with particular reference to its initiator, Lev Semenovich Berg (1876-1950). The differences between prevailing Russian and Western concepts of landscape in geography are discussed, and their common origins in German geographical thought in the late nineteenth and early twentieth centuries are delineated. It is argued that the principal differences are accounted for by a number of factors, of which Russia's own distinctive tradition in environmental science deriving from the work of V. V. Dokuchaev (1846-1903), the activities of certain key individuals (such as Berg and C. O. Sauer), and the very different social and political circumstances in different parts of the world appear to be the most significant. At the same time it is noted that neither in Russia nor in the West have geographers succeeded in specifying an agreed and unproblematic understanding of landscape, or more broadly in promoting a common geographical conception of human-environment relationships. In light of such uncertainties, the latter part of the article argues for closer international links between the variant landscape traditions in geography as an important contribution to the quest for sustainability