3,432 research outputs found
The nonperturbative propagator and vertex in massless quenched QED_d
It is well known how multiplicative renormalizability of the fermion
propagator, through its Schwinger-Dyson equation, imposes restrictions on the
3-point fermion-boson vertex in massless quenched quantum electrodynamics in
4-dimensions (QED). Moreover, perturbation theory serves as an excellent
guide for possible nonperturbative constructions of Green functions.
We extend these ideas to arbitrary dimensions . The constraint of
multiplicative renormalizability of the fermion propagator is generalized to a
Landau-Khalatnikov-Fradkin transformation law in -dimensions and it
naturally leads to a constraint on the fermion-boson vertex. We verify that
this constraint is satisfied in perturbation theory at the one loop level in
3-dimensions. Based upon one loop perturbative calculation of the vertex, we
find additional restrictions on its possible nonperturbative forms in arbitrary
dimensions.Comment: 13 pages, no figures, latex (uses IOP style files
Impact of Tandem Repeats on the Scaling of Nucleotide Sequences
Techniques such as detrended fluctuation analysis (DFA) and its extensions
have been widely used to determine the nature of scaling in nucleotide
sequences. In this brief communication we show that tandem repeats which are
ubiquitous in nucleotide sequences can prevent reliable estimation of possible
long-range correlations. Therefore, it is important to investigate the presence
of tandem repeats prior to scaling exponent estimation.Comment: 14 Pages, 3 Figure
Chiral Symmetry Breaking and Confinement Beyond Rainbow-Ladder Truncation
A non-perturbative construction of the 3-point fermion-boson vertex which
obeys its Ward-Takahashi or Slavnov-Taylor identity, ensures the massless
fermion and boson propagators transform according to their local gauge
covariance relations, reproduces perturbation theory in the weak coupling
regime and provides a gauge independent description for dynamical chiral
symmetry breaking (DCSB) and confinement has been a long-standing goal in
physically relevant gauge theories such as quantum electrodynamics (QED) and
quantum chromodynamics (QCD). In this paper, we demonstrate that the same
simple and practical form of the vertex can achieve these objectives not only
in 4-dimensional quenched QED (qQED4) but also in its 3-dimensional counterpart
(qQED3). Employing this convenient form of the vertex \emph{ansatz} into the
Schwinger-Dyson equation (SDE) for the fermion propagator, we observe that it
renders the critical coupling in qQED4 markedly gauge independent in contrast
with the bare vertex and improves on the well-known Curtis-Pennington
construction. Furthermore, our proposal yields gauge independent order
parameters for confinement and DCSB in qQED3.Comment: 8 pages, 6 figure
A fresh look at the (non-)Abelian Landau-Khalatnikov-Fradkin transformations
The Landau-Khalatnikov-Fradkin transformations (LKFTs) allow to interpolate
-point functions between different gauges. We first offer an alternative
derivation of these LKFTs for the gauge and fermions field in the Abelian (QED)
case when working in the class of linear covariant gauges. Our derivation is
based on the introduction of a gauge invariant transversal gauge field, which
allows a natural generalization to the non-Abelian (QCD) case of the LKFTs. To
our knowledge, within this rigorous formalism, this is the first construction
of the LKFTs beyond QED. The renormalizability of our setup is guaranteed to
all orders. We also offer a direct path integral derivation in the non-Abelian
case, finding full consistency.Comment: 16 page
Massive Dirac fermions and the zero field quantum Hall effect
Through an explicit calculation for a Lagrangian in quantum electrodynamics
in (2+1)-space--time dimensions (QED), making use of the relativistic Kubo
formula, we demonstrate that the filling factor accompanying the quantized
electrical conductivity for massive Dirac fermions of a single species in two
spatial dimensions is a half (in natural units) when time reversal and parity
symmetries of the Lagrangian are explicitly broken by the fermion mass term. We
then discuss the most general form of the QED Lagrangian, both for
irreducible and reducible representations of the Dirac matrices in the plane,
with emphasis on the appearance of a Chern-Simons term. We also identify the
value of the filling factor with a zero field quantum Hall effect (QHE).Comment: 15 pages. Accepted in Jour. Phys.
Landau-Khalatnikov-Fradkin Transformations and the Fermion Propagator in Quantum Electrodynamics
We study the gauge covariance of the massive fermion propagator in three as
well as four dimensional Quantum Electrodynamics (QED). Starting from its value
at the lowest order in perturbation theory, we evaluate a non-perturbative
expression for it by means of its Landau-Khalatnikov-Fradkin (LKF)
transformation. We compare the perturbative expansion of our findings with the
known one loop results and observe perfect agreement upto a gauge parameter
independent term, a difference permitted by the structure of the LKF
transformations.Comment: 9 pages, no figures, uses revte
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
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