218 research outputs found
O(1/N_f) Corrections to the Thirring Model in 2<d<4
The Thirring model, that is, a relativistic field theory of fermions with a
contact interaction between vector currents, is studied for dimensionalities
2<d<4 using the 1/N_f expansion, where N_f is the number of fermion species.
The model is found to have no ultraviolet divergences at leading order provided
a regularization respecting current conservation is used. Explicit O(1/N_f)
corrections are computed, and the model shown to be renormalizable at this
order in the massless limit; renormalizability appears to hold to all orders
due to a special case of Weinberg's theorem. This implies there is a universal
amplitude for four particle scattering in the asymptotic regime. Comparisons
are made with both the Gross-Neveu model and QED.Comment: 22 pages in plain TeX, with 7 figs included using psfig.tex (Minor
conceptual changes - algebra unaffected
The Landau gauge gluon and ghost propagator in the refined Gribov-Zwanziger framework in 3 dimensions
In previous works, we have constructed a refined version of the
Gribov-Zwanziger action in 4 dimensions, by taking into account a novel
dynamical effect. In this paper, we explore the 3-dimensional case. Analogously
as in 4 dimensions, we obtain a ghost propagator behaving like in the
infrared, while the gluon propagator reaches a finite nonvanishing value at
zero momentum. Simultaneously, a clear violation of positivity by the gluon
propagator is also found. This behaviour of the propagators turns out be in
agreement with the recent numerical simulations.Comment: 26 pages, 16 .eps figures. v3: version accepted for publication in
Phys Rev
Dynamical mass generation in quantum field theory : some methods with application to the Gross-Neveu model and Yang-Mills theory
We introduce some techniques to investigate dynamical mass generation. The
Gross-Neveu model (GN) is used as a toy model, because the GN mass gap is
exactly known, making it possible to check reliability of the various methods.
Very accurate results are obtained. Also application to SU(N) Yang-Mills (YM)
is discussed.Comment: 8 LaTeX2e pages, uses Kluwer class file crckbked.cls. Kluwer package
included. To appear in: Proceedings of the NATO Advanced Research Workshop on
"Confinement, Topology, and other Non-Perturbative Aspects of QCD", Stara
Lesna, Slovakia, 21-27 jan 200
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 renormalization group invariant scalar glueball operator in the (Refined) Gribov-Zwanziger framework
This paper presents a complete algebraic analysis of the renormalizability of
the operator in the Gribov-Zwanziger (GZ) formalism as
well as in the Refined Gribov-Zwanziger (RGZ) version. The GZ formalism offers
a way to deal with gauge copies in the Landau gauge. We explicitly show that
mixes with other gauge variant operators, and we determine
the mixing matrix to all orders, thereby only using algebraic arguments.
The mixing matrix allows us to uncover a renormalization group invariant
including the operator . With this renormalization group
invariant, we have paved the way for the study of the lightest scalar glueball
in the GZ formalism. We discuss how the soft breaking of the BRST symmetry of
the GZ action can influence the glueball correlation function. We expect
non-trivial mass scales, inherent to the GZ approach, to enter the pole
structure of this correlation function.Comment: 27 page
Universality and the magnetic catalysis of chiral symmetry breaking
The hypothesis that the magnetic catalysis of chiral symmetry breaking is due
to interactions of massless fermions in their lowest Landau level is examined
in the context of chirally symmetric models with short ranged interactions. It
is argued that, when the magnetic field is sufficiently large, even an
infinitesimal attractive interaction in the appropriate channel will break
chiral symmetry.Comment: 24 pages, 6 figures, REVTeX. The final version with minor
corrections. To appear in Phys Rev D60 (1999
Critical thermodynamics of three-dimensional chiral model for N > 3
The critical behavior of the three-dimensional -vector chiral model is
studied for arbitrary . The known six-loop renormalization-group (RG)
expansions are resummed using the Borel transformation combined with the
conformal mapping and Pad\'e approximant techniques. Analyzing the fixed point
location and the structure of RG flows, it is found that two marginal values of
exist which separate domains of continuous chiral phase transitions and where such
transitions are first-order. Our calculations yield and
. For the structure of RG flows is identical to
that given by the and 1/N expansions with the chiral fixed point
being a stable node. For the chiral fixed point turns out to be a
focus having no generic relation to the stable fixed point seen at small
and large . In this domain, containing the physical values and , phase trajectories approach the fixed point in a spiral-like
manner giving rise to unusual crossover regimes which may imitate varying
(scattered) critical exponents seen in numerous physical and computer
experiments.Comment: 12 pages, 3 figure
(Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap
We reconsider in some detail a construction allowing (Borel) convergence of
an alternative perturbative expansion, for specific physical quantities of
asymptotically free models. The usual perturbative expansions (with an explicit
mass dependence) are transmuted into expansions in 1/F, where
for while for m \lsim \Lambda,
being the basic scale and given by renormalization group
coefficients. (Borel) convergence holds in a range of which corresponds to
reach unambiguously the strong coupling infrared regime near , which
can define certain "non-perturbative" quantities, such as the mass gap, from a
resummation of this alternative expansion. Convergence properties can be
further improved, when combined with expansion (variationally improved
perturbation) methods. We illustrate these results by re-evaluating, from
purely perturbative informations, the O(N) Gross-Neveu model mass gap, known
for arbitrary from exact S matrix results. Comparing different levels of
approximations that can be defined within our framework, we find reasonable
agreement with the exact result.Comment: 33 pp., RevTeX4, 6 eps figures. Minor typos, notation and wording
corrections, 2 references added. To appear in Phys. Rev.
On ghost condensation, mass generation and Abelian dominance in the Maximal Abelian Gauge
Recent work claimed that the off-diagonal gluons (and ghosts) in pure
Yang-Mills theories, with Maximal Abelian gauge fixing (MAG), attain a
dynamical mass through an off-diagonal ghost condensate. This condensation
takes place due to a quartic ghost interaction, unavoidably present in MAG for
renormalizability purposes. The off-diagonal mass can be seen as evidence for
Abelian dominance. We discuss why ghost condensation of the type discussed in
those works cannot be the reason for the off-diagonal mass and Abelian
dominance, since it results in a tachyonic mass. We also point out what the
full mechanism behind the generation of a real mass might look like.Comment: 7 pages; uses revtex
Two loop effective potential for < A^2_\mu > in the Landau gauge in quantum chromodynamics
We construct the effective potential for the dimension two composite operator
1/2 A^{a 2}_\mu in QCD with massless quarks in the Landau gauge for an
arbitrary colour group at two loops. For SU(3) we show that an estimate for the
effective gluon mass decreases as N_f increases.Comment: 17 latex page
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