326 research outputs found
Multiplicative renormalizability of gluon and ghost propagators in QCD
We reformulate the coupled set of continuum equations for the renormalized
gluon and ghost propagators in QCD, such that the multiplicative
renormalizability of the solutions is manifest, independently of the specific
form of full vertices and renormalization constants. In the Landau gauge, the
equations are free of renormalization constants, and the renormalization point
dependence enters only through the renormalized coupling and the renormalized
propagator functions. The structure of the equations enables us to devise novel
truncations with solutions that are multiplicatively renormalizable and agree
with the leading order perturbative results. We show that, for infrared power
law behaved propagators, the leading infrared behavior of the gluon equation is
not solely determined by the ghost loop, as concluded in previous studies, but
that the gluon loop, the three-gluon loop, the four-gluon loop, and even
massless quarks also contribute to the infrared analysis. In our new Landau
gauge truncation, the combination of gluon and ghost loop contributions seems
to reject infrared power law solutions, but massless quark loops illustrate how
additional contributions to the gluon vacuum polarization could reinstate these
solutions. Moreover, a schematic study of the three-gluon and four-gluon loops
shows that they too need to be considered in more detail before a definite
conclusion about the existence of infrared power behaved gluon and ghost
propagators can be reached.Comment: 13 pages, 1 figure, submitted to Phys. Rev.
Gauge Dependence of Mass and Condensate in Chirally Asymmetric Phase of Quenched QED3
We study three dimensional quenched Quantum Electrodynamics in the bare
vertex approximation. We investigate the gauge dependence of the dynamically
generated Euclidean mass of the fermion and the chiral condensate for a wide
range of values of the covariant gauge parameter . We find that (i) away
from , gauge dependence of the said quantities is considerably reduced
without resorting to sophisticated vertex {\em ansatze}, (ii) wavefunction
renormalization plays an important role in restoring gauge invariance and (iii)
the Ward-Green-Takahashi identity seems to increase the gauge dependence when
used in conjunction with some simplifying assumptions. In the Landau gauge, we
also verify that our results are in agreement with those based upon dimensional
regularization scheme within the numerical accuracy available.Comment: 14 pages, 11 figures, uses revte
Constructing the fermion-boson vertex in QED3
We derive perturbative constraints on the transverse part of the
fermion-boson vertex in massive QED3 through its one loop evaluation in an
arbitrary covariant gauge. Written in a particular form, these constraints
naturally lead us to the first non-perturbative construction of the vertex,
which is in complete agreement with its one loop expansion in all momentum
regimes. Without affecting its one-loop perturbative properties, we also
construct an effective vertex in such a way that the unknown functions defining
it have no dependence on the angle between the incoming and outgoing fermion
momenta. Such a vertex should be useful for the numerical study of dynamical
chiral symmetry breaking, leading to more reliable results.Comment: 13 pages, 2 figure
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
Critical Statistical Charge for Anyonic Superconductivity
We examine a criterion for the anyonic superconductivity at zero temperature
in Abelian matter-coupled Chern-Simons gauge field theories in three
dimensions. By solving the Dyson-Schwinger equations, we obtain a critical
value of the statistical charge for the superconducting phase in a massless
fermion-Chern-Simons model.Comment: 11 pages; to appear in Phys Rev
Nonperturbative Renormalization and the QCD Vacuum
We present a self consistent approach to Coulomb gauge Hamiltonian QCD which
allows one to relate single gluon spectral properties to the long range
behavior of the confining interaction. Nonperturbative renormalization is
discussed. The numerical results are in good agreement with phenomenological
and lattice forms of the static potential.Comment: 23 pages in RevTex, 4 postscript figure
Constructing 3D crystal templates for photonic band gap materials using holographic optical tweezers
A simple and robust method is presented for the construction of 3-dimensional crystals from silica and polystyrene microspheres. The crystals are suitable for use as templates in the production of three-dimensional photonic band gap (PBG) materials. Manipulation of the microspheres was achieved using a dynamic holographic assembler (DHA) consisting of computer controlled holographic optical tweezers. Attachment of the microspheres was achieved by adjusting their colloidal interactions during assembly. The method is demonstrated by constructing a variety of 3-dimensional crystals using spheres ranging in size from 3 µm down to 800 nm. A major advantage of the technique is that it may be used to build structures that cannot be made using self-assembly. This is illustrated through the construction of crystals in which line defects have been deliberately included, and by building simple cubic structures
Renormalization and Chiral Symmetry Breaking in Quenched QED in Arbitrary Covariant Gauge
We extend a previous Landau-gauge study of subtractive renormalization of the
fermion propagator Dyson-Schwinger equation (DSE) in strong-coupling, quenched
QED_4 to arbitrary covariant gauges. We use the fermion-photon proper vertex
proposed by Curtis and Pennington with an additional correction term included
to compensate for the small gauge-dependence induced by the ultraviolet
regulator. We discuss the chiral limit and the onset of dynamical chiral
symmetry breaking in the presence of nonperturbative renormalization. We
extract the critical coupling in several different gauges and find evidence of
a small residual gauge-dependence in this quantity.Comment: REVTEX 3.0, 27 pages including 14 Extended Postscript files
comprising 9 figures. Replacement: discussion of chiral limit corrected, and
some minor typographical errors fixed. To appear in Phys. Rev.
Regularization-independent study of renormalized non-perturbative quenched QED
A recently proposed regularization-independent method is used for the first
time to solve the renormalized fermion Schwinger-Dyson equation numerically in
quenched QED. The Curtis-Pennington vertex is used to illustrate the
technique and to facilitate comparison with previous calculations which used
the alternative regularization schemes of modified ultraviolet cut-off and
dimensional regularization. Our new results are in excellent numerical
agreement with these, and so we can now conclude with confidence that there is
no residual regularization dependence in these results. Moreover, from a
computational point of view the regularization independent method has enormous
advantages, since all integrals are absolutely convergent by construction, and
so do not mix small and arbitrarily large momentum scales. We analytically
predict power law behaviour in the asymptotic region, which is confirmed
numerically with high precision. The successful demonstration of this efficient
new technique opens the way for studies of unquenched QED to be undertaken in
the near future.Comment: 20 pages,5 figure
Three point SUSY Ward identities without Ghosts
We utilise a non-local gauge transform which renders the entire action of
SUSY QED invariant and respects the SUSY algebra modulo the gauge-fixing
condition, to derive two- and three-point ghost-free SUSY Ward identities in
SUSY QED. We use the cluster decomposition principle to find the Green's
function Ward identities and then takes linear combinations of the latter to
derive identities for the proper functions.Comment: 20 pages, no figures, typos correcte
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