18 research outputs found
Non-perturbative Fermion Propagator for the Massless Quenched QED3
For massless quenched QED in three dimensions, we evaluate a non-perturbative
expression for the fermion propagator which agrees with its two loop
perturbative expansion in the weak coupling regime. This calculation is carried
out by making use of the Landau-Khalatnikov-Fradkin transformations. Any
improved construction of the fermion-boson vertex must make sure that the
solution of the Schwinger-Dyson equation for the fermion propagator reproduces
this result. For two different gauges, we plot the fermion propagator against
momentum. We then make a comparison with a similar plot, using the earlier
expression for the fermion propagator, which takes into account only the one
loop result.Comment: 11 pages, 3 figures, to appear in Phys. Lett.
The non-perturbative three-point vertex in massless quenched QED and perturbation theory constraints
Dong, Munczek and Roberts have shown how the full 3-point vertex that appears
in the Schwinger-Dyson equation for the fermion propagator can be expressed in
terms of a constrained function in massless quenched QED. However, this
analysis involved two key assumptions: that the fermion anomalous dimension
vanishes in the Landau gauge and that the transverse vertex has a simplified
dependence on momenta. Here we remove these assumptions and find the general
form for a new constrained function that ensures the multiplicative
renormalizability of the fermion propagator non-perturbatively. We then study
the restriction imposed on by recent perturbative calculations of the
vertex and compute its leading logarithmic expansion. Since should reduce
to this expansion in the weak coupling regime, this should serve as a guide to
its non-perturbative construction. We comment on the perturbative realization
of the constraints on .Comment: 18 pages, Latex, 2 figure
Causal construction of the massless vertex diagram
The massless one-loop vertex diagram is constructed by exploiting the causal
structure of the diagram in configuration space, which can be translated
directly into dispersive relations in momentum space.Comment: 14 pages, LATEX with style file, corresponds to published versio
Constraint on the QED Vertex from the Mass Anomalous Dimension
We discuss the structure of the non-perturbative fermion-boson vertex in
quenched QED. We show that it is possible to construct a vertex which not only
ensures that the fermion propagator is multiplicatively renormalizable, obeys
the appropriate Ward-Takahashi identity, reproduces perturbation theory for
weak couplings and guarantees that the critical coupling at which the mass is
dynamically generated is gauge independent but also makes sure that the value
for the anomalous dimension for the mass function is strictly 1, as Holdom and
Mahanta have proposed.Comment: 8 pages, LaTeX, October 199
Longitudinal and transverse fermion-boson vertex in QED at finite temperature in the HTL approximation
We evaluate the fermion-photon vertex in QED at the one loop level in Hard
Thermal Loop approximation and write it in covariant form. The complete vertex
can be expanded in terms of 32 basis vectors. As is well known, the
fermion-photon vertex and the fermion propagator are related through a
Ward-Takahashi Identity (WTI). This relation splits the vertex into two parts:
longitudinal (Gamma_L) and transverse (Gamma_T). Gamma_L is fixed by the WTI.
The description of the longitudinal part consumes 8 of the basis vectors. The
remaining piece Gamma_T is then written in terms of 24 spin amplitudes.
Extending the work of Ball and Chiu and Kizilersu et. al., we propose a set of
basis vectors T^mu_i(P_1,P_2) at finite temperature such that each of these is
transverse to the photon four-momentum and also satisfies T^mu_i(P,P)=0, in
accordance with the Ward Identity, with their corresponding coefficients being
free of kinematic singularities. This basis reduces to the form proposed by
Kizilersu et. al. at zero temperature. We also evaluate explicitly the
coefficient of each of these vectors at the above-mentioned level of
approximation.Comment: 13 pages, uses RevTe
ONE LOOP QED VERTEX IN ANY COVARIANT GAUGE: ITS COMPLETE ANALYTIC FORM
The one loop vertex in QED is calculated in arbitrary covariant gauges as an
analytic function of its momenta. The vertex is decomposed into a longitudinal
part, that is fully responsible for ensuring the Ward and Ward-Takahashi
identities are satisfied, and a transverse part. The transverse part is
decomposed into 8 independent components each being separately free of
kinematic singularities in covariant gauge in a basis that modifies
that proposed by Ball and Chiu. Analytic expressions for all 11 components of
the vertex are given explicitly in terms of elementary functions
and one Spence function. These results greatly simplify in particular kinematic
regimes.Comment: 35 pages, latex, 2 figures, Complete postscript file available from:
ftp://cpt1.dur.ac.uk/pub/preprints/dtp95/dtp9506/dtp9406.p
Nonperturbative structure of the quark-gluon vertex
The complete tensor structure of the quark--gluon vertex in Landau gauge is
determined at two kinematical points (`asymmetric' and `symmetric') from
lattice QCD in the quenched approximation. The simulations are carried out at
beta=6.0, using a mean-field improved Sheikholeslami-Wohlert fermion action,
with two quark masses ~ 60 and 115 MeV. We find substantial deviations from the
abelian form at the asymmetric point. The mass dependence is found to be
negligible. At the symmetric point, the form factor related to the
chromomagnetic moment is determined and found to contribute significantly to
the infrared interaction strength.Comment: 16 pages, 11 figures, JHEP3.cl
Two-loop three-gluon vertex in zero-momentum limit
The two-loop three-gluon vertex is calculated in an arbitrary covariant
gauge, in the limit when one of the external momenta vanishes. The differential
Ward-Slavnov-Taylor (WST) identity related to this limit is discussed, and the
relevant results for the ghost-gluon vertex and two-point functions are
obtained. Together with the differential WST identity, they provide another
independent way for calculating the three-gluon vertex. The renormalization of
the results obtained is also presented.Comment: 22 pages, LaTeX, including 4 figures, uses eps
Three-gluon vertex in arbitrary gauge and dimension
One-loop off-shell contributions to the three-gluon vertex are calculated, in
arbitrary covariant gauge and in arbitrary space-time dimension, including
quark-loop contributions (with massless quarks). It is shown how one can get
the results for all on-shell limits of interest directly from the general
off-shell expression. The corresponding general expressions for the one-loop
ghost-gluon vertex are also obtained. They allow for a check of consistency
with the Ward--Slavnov--Taylor identity.Comment: 41 pages, LaTex, plus 3 figures in separate file. Misprints (signs)
in eqs.(4.26), (C.2), (C.4), (C.5) are corrected. To appear in Phys. Rev.