17,407 research outputs found
Unified description of seagull cancellations and infrared finiteness of gluon propagators
We present a generalized theoretical framework for dealing with the important
issue of dynamical mass generation in Yang-Mills theories, and, in particular,
with the infrared finiteness of the gluon propagators, observed in a multitude
of recent lattice simulations. Our analysis is manifestly gauge-invariant, in
the sense that it preserves the transversality of the gluon self-energy, and
gauge-independent, given that the conclusions do not depend on the choice of
the gauge-fixing parameter within the linear covariant gauges. The central
construction relies crucially on the subtle interplay between the Abelian Ward
identities satisfied by the nonperturbative vertices and a special integral
identity that enforces a vast number of 'seagull cancellations' among the one-
and two-loop dressed diagrams of the gluon Schwinger-Dyson equation. The key
result of these considerations is that the gluon propagator remains rigorously
massless, provided that the vertices do not contain (dynamical) massless poles.
When such poles are incorporated into the vertices, under the pivotal
requirement of respecting the gauge symmetry of the theory, the terms
comprising the Ward identities conspire in such a way as to still enforce the
total annihilation of all quadratic divergences, inducing, at the same time,
residual contributions that account for the saturation of gluon propagators in
the deep infrared.Comment: 40 pages, 7 figures; v2: typos corrected, version matching the
published on
Evidence of ghost suppression in gluon mass dynamics
In this work we study the impact that the ghost sector of pure Yang-Mills
theories may have on the generation of a dynamical gauge boson mass, which
hinges on the appearance of massless poles in the fundamental vertices of the
theory, and the subsequent realization of the well-known Schwinger mechanism.
The process responsible for the formation of such structures is itself
dynamical in nature, and is governed by a set of Bethe-Salpeter type of
integral equations. While in previous studies the presence of massless poles
was assumed to be exclusively associated with the background-gauge three-gluon
vertex, in the present analysis we allow them to appear also in the
corresponding ghost-gluon vertex. The full analysis of the resulting
Bethe-Salpeter system reveals that the contribution of the poles associated
with the ghost-gluon vertex are particularly suppressed, their sole discernible
effect being a slight modification in the running of the gluon mass, for
momenta larger than a few GeV. In addition, we examine the behavior of the
(background-gauge) ghost-gluon vertex in the limit of vanishing ghost momentum,
and derive the corresponding version of Taylor's theorem. These considerations,
together with a suitable Ansatz, permit us the full reconstruction of the pole
sector of the two vertices involved.Comment: 30 pages, 10 figure
Phenomenological Renormalization Group Methods
Some renormalization group approaches have been proposed during the last few
years which are close in spirit to the Nightingale phenomenological procedure.
In essence, by exploiting the finite size scaling hypothesis, the approximate
critical behavior of the model on infinite lattice is obtained through the
exact computation of some thermal quantities of the model on finite clusters.
In this work some of these methods are reviewed, namely the mean field
renormalization group, the effective field renormalization group and the finite
size scaling renormalization group procedures. Although special emphasis is
given to the mean field renormalization group (since it has been, up to now,
much more applied an extended to study a wide variety of different systems) a
discussion of their potentialities and interrelations to other methods is also
addressed.Comment: Review Articl
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