881 research outputs found
Comment on ``Reduction of static field equation of Faddeev model to first order PDE'', arXiv:0707.2207
The authors of the article Phys. Lett. B 652 (2007) 384, (arXiv:0707.2207),
propose an interesting method to solve the Faddeev model by reducing it to a
set of first order PDEs. They first construct a vectorial quantity , depending on the original field and its first derivatives, in terms of which
the field equations reduce to a linear first order equation. Then they find
vectors and which identically obey this linear
first order equation. The last step consists in the identification of the with the original as a function of the original field.
Unfortunately, the derivation of this last step in the paper cited above
contains an error which invalidates most of its results
Cosmological tensor perturbations in the Randall-Sundrum model: evolution in the near-brane limit
We discuss the evolution of cosmological tensor perturbations in the RSII
model. In Gaussian normal coordinates the wave equation is non-separable, so we
use the near-brane limit to perform the separation and study the evolution of
perturbations. Massive excitations, which may also mix, decay outside the
horizon which could lead to some novel cosmological signatures.Comment: 18 pages, 1 figur
A Skyrme-type proposal for baryonic matter
The Skyrme model is a low-energy effective field theory for QCD, where the
baryons emerge as soliton solutions. It is, however, not so easy within the
standard Skyrme model to reproduce the almost exact linear growth of the
nuclear masses with the baryon number (topological charge), due to the lack of
Bogomolny solutions in this model, which has also hindered analytical progress.
Here we identify a submodel within the Skyrme-type low energy effective action
which does have a Bogomolny bound and exact Bogomolny solutions, and therefore,
at least at the classical level, reproduces the nuclear masses by construction.
Due to its high symmetry, this model qualitatively reproduces the main features
of the liquid droplet model of nuclei. Finally, we discuss under which
circumstances the proposed sextic term, which is of an essentially geometric
and topological nature, can be expected to give a reasonable description of
properties of nuclei.Comment: 11 pages, 2 figures, latex. v3: Extended and revised version, some
clarifications added. Some references and 2 figures added. v4: matches
published versio
Hopf instantons and the Liouville equation in target space
We generalise recent results on Hopf instantons in a Chern--Simons and
Fermion theory in a fixed background magnetic field. We find that these
instanton solutions have to obey the Liouville equation in target space. As a
consequence, these solutions are given by a class of Hopf maps that consist of
the composition of the standard Hopf map with an arbitrary rational map.Comment: Latex file, 11 pages, no figure
Normal Mode Spectrum of the Deuteron in the Skyrme Model
The normal mode spectrum of the deuteron in the Skyrme model is computed. We
find a bound doublet mode below the pion mass, which can be related to the
well-known scattering of two skyrmions. We also find a singlet
`breather' mode and another doublet above the pion mass. The qualitative
pattern of the spectrum is similar to that recently found for the B=4
multiskyrmion. The symmetries of all the vibrational modes are presented.Comment: LaTeX, 10 pages, 3 figure
On Chiral Symmetry Restoration at Finite Density in Large N_c QCD
At large N_c, cold nuclear matter is expected to form a crystal and thus
spontaneously break translational symmetry. The description of chiral symmetry
breaking and translational symmetry breaking can become intertwined. Here, the
focus is on aspects of chiral symmetry breaking and its possible restoration
that are by construction independent of the nature of translational symmetry
breaking---namely spatial averages of chiral order parameters. A system will be
considered to be chirally restored provided all spatially-averaged chiral order
parameters are zero. A critical question is whether chiral restoration in this
sense is possible for phases in which chiral order parameters are locally
non-zero but whose spatial averages all vanish. We show that this is not
possible unless all chirally-invariant observables are spatially uniform. This
result is first derived for Skyrme-type models, which are based on a nonlinear
sigma model and by construction break chiral symmetry on a point-by-point
basis. A no-go theorem for chiral restoration (in the average sense) for all
models of this type is obtained by showing that in these models there exist
chirally symmetric order parameters which cannot be spatially uniform. Next we
show that the no-go theorem applies to large N_c QCD in any phase which has a
non-zero but spatially varying chiral condensate. The theorem is demonstrated
by showing that in a putative chirally-restored phase, the field configuration
can be reduced to that of a nonlinear sigma model.Comment: 12 pages, 1 tabl
Poly-essential and general Hyperelastic World (brane) models
This article provides a unified treatment of an extensive category of
non-linear classical field models whereby the universe is represented (perhaps
as a brane in a higher dimensional background) in terms of a structure of a
mathematically convenient type describable as hyperelastic, for which a
complete set of equations of motion is provided just by the energy-momentum
conservation law. Particular cases include those of a perfect fluid in
quintessential backgrounds of various kinds, as well as models of the elastic
solid kind that has been proposed to account for cosmic acceleration. It is
shown how an appropriately generalised Hadamard operator can be used to
construct a symplectic structure that controles the evolution of small
perturbations, and that provides a characteristic equation governing the
propagation of weak discontinuities of diverse (extrinsic and extrinsic) kinds.
The special case of a poly-essential model - the k-essential analogue of an
ordinary polytropic fluid - is examined and shown to be well behaved (like the
fluid) only if the pressure to density ratio is positive.Comment: 16 pages Latex, Contrib. to 10th Peyresq Pysics Meeting, June 2005:
Micro and Macro Structures of Spacetim
A Quintessence Scalar Field in Brans-Dicke Theory
It is shown that a minimally coupled scalara field in Brans-Dicke theory
yields a non-decelerated expansion for the present universe for open, flat and
closed Friedmann-Robertson-Walker models.Comment: Latex file, 9 pages, no figures; to be published in Classical and
Quantum Gravit
Symmetric Skyrmions
We present candidates for the global minimum energy solitons of charge one to
nine in the Skyrme model, generated using sophisticated numerical algorithms.
Assuming the Skyrme model accurately represents the low energy limit of QCD,
these configurations correspond to the classical nuclear ground states of the
light elements. The solitons found are particularly symmetric, for example, the
charge seven skyrmion has icosahedral symmetry, and the shapes are shown to fit
a remarkable sequence defined by a geometric energy minimization (GEM) rule. We
also calculate the energies and sizes to within at least a few percent
accuracy. These calculations provide the basis for a future investigation of
the low energy vibrational modes of skyrmions and hence the possibility of
testing the Skyrme model against experiment.Comment: latex, 9 pages, 1 figure (fig1.gif
Hopf instantons in Chern-Simons theory
We study an Abelian Chern-Simons and Fermion system in three dimensions. In
the presence of a fixed prescribed background magnetic field we find an
infinite number of fully three-dimensional solutions. These solutions are
related to Hopf maps and are, therefore, labelled by the Hopf index. Further we
discuss the interpretation of the background field.Comment: one minor error corrected, discussion of gauge fixing added, some
references adde
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