1,277 research outputs found
Generalised Fourier Transform and Perturbations to Soliton Equations
A brief survey of the theory of soliton perturbations is presented. The focus
is on the usefulness of the so-called Generalised Fourier Transform (GFT). This
is a method that involves expansions over the complete basis of `squared
olutions` of the spectral problem, associated to the soliton equation. The
Inverse Scattering Transform for the corresponding hierarchy of soliton
equations can be viewed as a GFT where the expansions of the solutions have
generalised Fourier coefficients given by the scattering data.
The GFT provides a natural setting for the analysis of small perturbations to
an integrable equation: starting from a purely soliton solution one can
`modify` the soliton parameters such as to incorporate the changes caused by
the perturbation.
As illustrative examples the perturbed equations of the KdV hierarchy, in
particular the Ostrovsky equation, followed by the perturbation theory for the
Camassa- Holm hierarchy are presented.Comment: 20 pages, no figures, to appear in: Discrete and Continuous Dynamical
Systems
The local phase transitions of the solvent in the neighborhood of a solvophobic polymer at high pressures
We investigate local phase transitions of the solvent in the neighborhood of
a solvophobic polymer chain which is induced by a change of the polymer-solvent
repulsion and the solvent pressure in the bulk solution. We describe the
polymer in solution by the Edwards model, where the conditional partition
function of the polymer chain at a fixed radius of gyration is described by a
mean-field theory. The contributions of the polymer-solvent and the
solvent-solvent interactions to the total free energy are described within the
mean-field approximation. We obtain the total free energy of the solution as a
function of the radius of gyration and the average solvent number density
within the gyration volume. The resulting system of coupled equations is solved
varying the polymer-solvent repulsion strength at high solvent pressure in the
bulk. We show that the coil-globule (globule-coil) transition occurs
accompanied by a local solvent evaporation (condensation) within the gyration
volum
External leg amputation in conformal invariant three-point function
Amputation of external legs is carried out explicitly for the conformal
invariant three-point function involving two spinors and one vector field. Our
results are consistent with the general result that amputing an external leg in
a conformal invariant Green function replaces a field by its conformal partner
in the Green function. A new star-triangle relation, involving two spinors and
one vector field, is derived and used for the calculation.Comment: 16 pages; last paragraph added in Sec. 10, presentation improved, to
appear in Eur. Phys. J.
Big Corrections from a Little Higgs
We calculate the tree-level expressions for the electroweak precision
observables in the SU(5)/SO(5) littlest Higgs model. The source for these
corrections are the exchange of heavy gauge bosons, explicit corrections due to
non-linear sigma-model dynamics and a triplet Higgs VEV. Weak isospin violating
contributions are present because there is no custodial SU(2) global symmetry.
The bulk of these weak isospin violating corrections arise from heavy gauge
boson exchange while a smaller contribution comes from the triplet Higgs VEV. A
global fit is performed to the experimental data and we find that throughout
the parameter space the symmetry breaking scale is bounded by f > 4 TeV at 95%
C.L. Stronger bounds on f are found for generic choices of the high energy
gauge couplings. We find that even in the best case scenario one would need
fine tuning of less than a percent to get a Higgs mass as light as 200 GeV.Comment: 20 pages, 5 figures included, typos fixed, comments on the effects of
extra vector-like heavy fermions adde
A Study of the Kazakov-Migdal Model
We study numerically the SU(2) Kazakov-Migdal model of `induced QCD'. In
contrast to our earlier work on the subject we have chosen here {\it not} to
integrate out the gauge fields but to keep them in the Monte Carlo simulation.
This allows us to measure observables associated with the gauge fields and
thereby address the problem of the local symmetry present in the model.
We confirm our previous result that the model has a line of first order phase
transitions terminating in a critical point. The adjoint plaquette has a clear
discontinuity across the phase transition, whereas the plaquette in the
fundamental representation is always zero in accordance with Elitzur's theorem.
The density of small monopoles shows very little variation and is always
large. We also find that the model has extra local U(1) symmetries which do not
exist in the case of the standard adjoint theory. As a result, we are able to
show that two of the angles parameterizing the gauge field completely decouple
from the theory and the continuum limit defined around the critical point can
therefore not be `QCD'.Comment: 11 pages, UTHEP-24
What if the Higgs couplings to W and Z bosons are larger than in the Standard Model?
We derive a general sum rule relating the Higgs coupling to W and Z bosons to
the total cross section of longitudinal gauge boson scattering in I=0,1,2
isospin channels. The Higgs coupling larger than in the Standard Model implies
enhancement of the I=2 cross section. Such an enhancement could arise if the
Higgs sector is extended by an isospin-2 scalar multiplet including a doubly
charged, singly charged, and another neutral Higgs.Comment: 11 pages, no figures. v2: comments and references added. v3: early
QCD references adde
Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces
A special class of integrable nonlinear differential equations related to
A.III-type symmetric spaces and having additional reductions are analyzed via
the inverse scattering method (ISM). Using the dressing method we construct two
classes of soliton solutions associated with the Lax operator. Next, by using
the Wronskian relations, the mapping between the potential and the minimal sets
of scattering data is constructed. Furthermore, completeness relations for the
'squared solutions' (generalized exponentials) are derived. Next, expansions of
the potential and its variation are obtained. This demonstrates that the
interpretation of the inverse scattering method as a generalized Fourier
transform holds true. Finally, the Hamiltonian structures of these generalized
multi-component Heisenberg ferromagnetic (MHF) type integrable models on
A.III-type symmetric spaces are briefly analyzed
Negative s and Light New Physics
Motivated by the difference between SLD's recent measurement of ALR and the
corresponding LEP results, we explore which kinds of new particles can (1)
contribute dominantly to new physics through oblique corrections, (2) produce
negative values for S and T, and (3) not be in conflict with any other
experiments, on or off the Z resonance. We are typically led to models which
involve new particles which are not much heavier than MZ/2, and so which may
also have implications for other experiments in the near future. For such light
particles, we show how the oblique-parameter analysis of purely Z-pole data
requires the interpretation of the data in terms of modified parameters, S' and
T', whose difference from S and T improves the available parameter space of the
models.Comment: plain TeX, 16 pages, 6 figures attached as a uuencoded file,
McGill-94/27, NEIP-94-00
The Pole Mass of The Heavy Quark. Perturbation Theory and Beyond
The key quantity of the heavy quark theory is the quark mass . Since
quarks are unobservable one can suggest different definitions of . One of
the most popular choices is the pole quark mass routinely used in perturbative
calculations and in some analyses based on heavy quark expansions. We show that
no precise definition of the pole mass can be given in the full theory once
non-perturbative effects are included. Any definition of this quantity suffers
from an intrinsic uncertainty of order \Lam /m_Q. This fact is succinctly
described by the existence of an infrared renormalon generating a factorial
divergence in the high-order coefficients of the series; the
corresponding singularity in the Borel plane is situated at . A
peculiar feature is that this renormalon is not associated with the matrix
element of a local operator. The difference \La \equiv M_{H_Q}-m_Q^{pole} can
still be defined in Heavy Quark Effective Theory, but only at the price of
introducing an explicit dependence on a normalization point : \La (\mu
). Fortunately the pole mass {\em per se} does not appear in
calculable observable quantities.Comment: 22 pages, Latex, 6 figures (available upon request), TPI-MINN-94/4-T,
CERN-TH.7171/94, UND-HEP-94-BI
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