66 research outputs found
Anomalies in Ward Identities for Three-Point Functions Revisited
A general calculational method is applied to investigate symmetry relations
among divergent amplitudes in a free fermion model. A very traditional work on
this subject is revisited. A systematic study of one, two and three point
functions associated to scalar, pseudoscalar, vector and axial-vector densities
is performed. The divergent content of the amplitudes are left in terms of five
basic objects (external momentum independent). No specific assumptions about a
regulator is adopted in the calculations. All ambiguities and symmetry
violating terms are shown to be associated with only three combinations of the
basic divergent objects. Our final results can be mapped in the corresponding
Dimensional Regularization calculations (in cases where this technique could be
applied) or in those of Gertsein and Jackiw which we will show in detail. The
results emerging from our general approach allow us to extract, in a natural
way, a set of reasonable conditions (e.g. crucial for QED consistency) that
could lead us to obtain all Ward Identities satisfied. Consequently, we
conclude that the traditional approach used to justify the famous triangular
anomalies in perturbative calculations could be questionable. An alternative
point of view, dismissed of ambiguities, which lead to a correct description of
the associated phenomenology, is pointed out.Comment: 26 pages, Revtex, revised version, Refs. adde
Hadronic current correlation functions at finite temperature in the NJL model
Recently there have been suggestions that for a proper description of
hadronic matter and hadronic correlation functions within the NJL model at
finite density/temperature the parameters of the model should be taken
density/temperature dependent. Here we show that qualitatively similar results
can be obtained using a cutoff-independent regularization of the NJL model. In
this regularization scheme one can express the divergent parts at finite
density/temperature of the amplitudes in terms of their counterparts in vacuum.Comment: Presented at 9th Hadron Physics and 8th Relativistic Aspects of
Nuclear Physics (HADRON-RANP 2004): A Joint Meeting on QCD and QGP, Angra dos
Reis, Rio de Janeiro, Brazil, 28 Mar - 3 Apr 200
Consistency in Perturbative Calculations and Radiatively Induced Lorentz and CPT Violations
The origin of the radiatively induced Lorentz and CPT violations, in
perturbative evaluations, of an extended version of QED, is investigated. Using
a very general calculational method, concerning the manipulations and
calculations involving divergent amplitudes, we clearly identify the possible
sources of contributions for the violating terms. We show that consistency in
the perturbative calculations, in a broader sense, leaves no room for the
existence of radiatively induced contributions which is in accordance with what
was previously conjectured and recently advocated by some authors supported on
general arguments.Comment: 8 pages, Revte
Cutoff-independent regularization of four-fermion interactions for color superconductivity
We implement a cutoff-independent regularization of four-fermion interactions
to calculate the color-superconducting gap parameter in quark matter. The
traditional cutoff regularization has difficulties for chemical potentials \mu
of the order of the cutoff \Lambda, predicting in particular a vanishing gap at
\mu \sim \Lambda. The proposed cutoff-independent regularization predicts a
finite gap at high densities and indicates a smooth matching with the weak
coupling QCD prediction for the gap at asymptotically high densities.Comment: 5 pages, 1 eps figure - Revised manuscript to match the published
pape
From arbitrariness to ambiguities in the evaluation of perturbative physical amplitudes and their symmetry relations
A very general calculational strategy is applied to the evaluation of the
divergent physical amplitudes which are typical of perturbative calculations.
With this approach in the final results all the intrinsic arbitrariness of the
calculations due to the divergent character is still present. We show that by
using the symmetry properties as a guide to search for the (compulsory) choices
in such a way as to avoid ambiguities, a deep and clear understanding of the
role of regularization methods emerges. Requiring then an universal point of
view for the problem, as allowed by our approach, very interesting conclusions
can be stated about the possible justifications of most intriguing aspect of
the perturbative calculations in quantum field theory: the triangle anomalies.Comment: 16 pages, no figure
Consistency in Regularizations of the Gauged NJL Model at One Loop Level
In this work we revisit questions recently raised in the literature
associated to relevant but divergent amplitudes in the gauged NJL model. The
questions raised involve ambiguities and symmetry violations which concern the
model's predictive power at one loop level. Our study shows by means of an
alternative prescription to handle divergent amplitudes, that it is possible to
obtain unambiguous and symmetry preserving amplitudes. The procedure adopted
makes use solely of {\it general} properties of an eventual regulator, thus
avoiding an explicit form. We find, after a thorough analysis of the problem
that there are well established conditions to be fulfiled by any consistent
regularization prescription in order to avoid the problems of concern at one
loop level.Comment: 22 pages, no figures, LaTeX, to appear in Phys.Rev.
A predictive formulation of the Nambu--Jona-Lasinio model
A novel strategy to handle divergences typical of perturbative calculations
is implemented for the Nambu--Jona-Lasinio model and its phenomenological
consequences investigated. The central idea of the method is to avoid the
critical step involved in the regularization process, namely the explicit
evaluation of divergent integrals. This goal is achieved by assuming a
regularization distribution in an implicit way and making use, in intermediary
steps, only of very general properties of such regularization. The finite parts
are separated of the divergent ones and integrated free from effects of the
regularization. The divergent parts are organized in terms of standard objects
which are independent of the (arbitrary) momenta running in internal lines of
loop graphs. Through the analysis of symmetry relations, a set of properties
for the divergent objects are identified, which we denominate consistency
relations, reducing the number of divergent objects to only a few ones. The
calculational strategy eliminates unphysical dependencies of the arbitrary
choices for the routing of internal momenta, leading to ambiguity-free, and
symmetry-preserving physical amplitudes. We show that the imposition of scale
properties for the basic divergent objects leads to a critical condition for
the constituent quark mass such that the remaining arbitrariness is removed.
The model become predictive in the sense that its phenomenological consequences
do not depend on possible choices made in intermediary steps. Numerical results
are obtained for physical quantities at the one-loop level for the pion and
sigma masses and pion-quark and sigma-quark coupling constants.Comment: 38 pages, 1 figure, To appear in Phy.Rev.
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