60 research outputs found
On the existence of finite-energy lumps in classic field theories
We show how the existence of non-trivial finite-energy time-dependent
classical lumps is restricted by a generalized virial theorem. For simple model
Lagrangians, bounds on energies follow.Comment: 4 pages, 1 figure; substantial change
Real null coframes in general relativity and GPS type coordinates
Based on work of Derrick, Coll, and Morales, we define a `symmetric' null
coframe with {\it four real null covectors}. We show that this coframe is
closely related to the GPS type coordinates recently introduced by Rovelli.Comment: Latex script, 9 pages, 4 figures; references added to work of
Derrick, Coll, and Morales, 1 new figur
Electrodynamic Limit in a Model for Charged Solitons
We consider a model of topological solitons where charged particles have
finite mass and the electric charge is quantised already at the classical
level. In the electrodynamic limit, which physically corresponds to
electrodynamics of solitons of zero size, the Lagrangian of this model has two
degrees of freedom only and reduces to the Lagrangian of the Maxwell field in
dual representation. We derive the equations of motion and discuss their
relations with Maxwell's equations. It is shown that Coulomb and Lorentz forces
are a consequence of topology. Further, we relate the U(1) gauge invariance of
electrodynamics to the geometry of the soliton field, give a general relation
for the derivation of the soliton field from the field strength tensor in
electrodynamics and use this relation to express homogeneous electric fields in
terms of the soliton field.Comment: 13 pages, 4 figures, Introduction and Section II (Model Lagrangian)
rewritten, new chapters concerning electrodynamic limit and discussion of
causality inserte
Non-topological solitons in brane world models
We examine some general properties of a certain class of scalar filed theory
models containing non-topological soliton solutions in the context of brane
world models with compact large extra dimensions. If a scalar field is allowed
to propagate in extra space, then, beside standard Kaluza-Klein type
excitations, a whole new class of very massive soliton-type states can exist.
Depending on their abundance, they can be important dark matter candidates or
give significant contribution to entropy and energy density in our universe. .Comment: version accepted for publication in Physical Review
On the Strong Coupling Limit of the Faddeev-Hopf Model
The variational calculus for the Faddeev-Hopf model on a general Riemannian
domain, with general Kaehler target space, is studied in the strong coupling
limit. In this limit, the model has key similarities with pure Yang-Mills
theory, namely conformal invariance in dimension 4 and an infinite dimensional
symmetry group. The first and second variation formulae are calculated and
several examples of stable solutions are obtained. In particular, it is proved
that all immersive solutions are stable. Topological lower energy bounds are
found in dimensions 2 and 4. An explicit description of the spectral behaviour
of the Hopf map S^3 -> S^2 is given, and a conjecture of Ward concerning the
stability of this map in the full Faddeev-Hopf model is proved.Comment: 21 pages, 0 figure
A String Approximation for Cooper Pair in High-T superconductivity
It is assumed that in some sense the High-T superconductivity is similar
to the quantum chromodynamics (QCD). This means that the phonons in High-T
superconductor have the strong interaction between themselves like to gluons in
the QCD. At the experimental level this means that in High-T superconductor
exists the nonlinear sound waves. It is possible that the existence of the
strong phonon-phonon interaction leads to the confinement of phonons into a
phonon tube (PT) stretched between two Cooper electrons like a hypothesized
flux tube between quark and antiquark in the QCD. The flux tube in the QCD
brings to a very strong interaction between quark-antiquark, the similar
situation can be in the High-T superconductor: the presence of the PT can
essentially increase the binding energy for the Cooper pair. In the first rough
approximation the PT can be approximated as a nonrelativistic string with
Cooper electrons at the ends. The BCS theory with such potential term is
considered. It is shown that Green's function method in the superconductivity
theory is a realization of discussed Heisenberg idea proposed by him for the
quantization of nonlinear spinor field. A possible experimental testing for the
string approximation of the Cooper pair is offered.Comment: Essential changes: (a) the section is added in which it is shown that
Green's function method in the superconductivity theory is a realization of
discussed Heisenberg quantization method; (b) Veneziano amplitude is
discussed as an approximation for the 4-point Green's function in High-T_c;
(c) it is shown that Eq.(53) has more natural solution on the layer rather
than on 3 dimensional spac
O(4) texture with a cosmological constant
We investigate O(4) textures in a background with a positive cosmological
constant. We find static solutions which co-move with the expanding background.
There exists a solution in which the scalar field is regular at the horizon.
This solution has a noninteger winding number smaller than one. There also
exist solutions in which scalar-field derivatives are singular at the horizon.
Such solutions can complete one winding within the horizon. If the winding
number is larger than some critical value, static solutions including the
regular one are unstable under perturbations.Comment: 25 pages, revtex, 6 eps figure
Scalar Solitons on the Fuzzy Sphere
We study scalar solitons on the fuzzy sphere at arbitrary radius and
noncommutativity. We prove that no solitons exist if the radius is below a
certain value. Solitons do exist for radii above a critical value which depends
on the noncommutativity parameter. We construct a family of soliton solutions
which are stable and which converge to solitons on the Moyal plane in an
appropriate limit. These solutions are rotationally symmetric about an axis and
have no allowed deformations. Solitons that describe multiple lumps on the
fuzzy sphere can also be constructed but they are not stable.Comment: 24 pages, 2 figures, typo corrected and stylistic changes. v3:
reference adde
Polar Perturbations of Self-gravitating Supermassive Global Monopoles
Spontaneous global symmetry breaking of O(3) scalar field gives rise to
point-like topological defects, global monopoles. By taking into account
self-gravity,the qualitative feature of the global monopole solutions depends
on the vacuum expectation value v of the scalar field. When v < sqrt{1 / 8 pi},
there are global monopole solutions which have a deficit solid angle defined at
infinity. When sqrt{1 / 8 pi} <= v < sqrt{3 / 8 pi}, there are global monopole
solutions with the cosmological horizon, which we call the supermassive global
monopole. When v >= sqrt{3 / 8 pi}, there is no nontrivial solution. It was
shown that all of these solutions are stable against the spherical
perturbations. In addition to the global monopole solutions, the de Sitter
solutions exist for any value of v. They are stable against the spherical
perturbations when v sqrt{3 / 8 pi}.
We study polar perturbations of these solutions and find that all
self-gravitating global monopoles are stable even against polar perturbations,
independently of the existence of the cosmological horizon, while the de Sitter
solutions are always unstable.Comment: 10 pages, 6 figures, corrected some type mistakes (already corrected
in PRD version
Low Temperature Static and Dynamic Behavior of the Two-Dimensional Easy-Axis Heisenberg Model
We apply the self-consistent harmonic approximation (SCHA) to study static
and dynamic properties of the two-dimensional classical Heisenberg model with
easy-axis anisotropy. The static properties obtained are magnetization and spin
wave energy as functions of temperature, and the critical temperature as a
function of the easy-axis anisotropy. We also calculate the dynamic correlation
functions using the SCHA renormalized spin wave energy. Our analytical results,
for both static properties and dynamic correlation functions, are compared to
numerical simulation data combining cluster-Monte Carlo algorithms and Spin
Dynamics. The comparison allows us to conclude that far below the transition
temperature, where the SCHA is valid, spin waves are responsible for all
relevant features observed in the numerical simulation data; topological
excitations do not seem to contribute appreciably. For temperatures closer to
the transition temperature, there are differences between the dynamic
correlation functions from SCHA theory and Spin Dynamics; these may be due to
the presence of domain walls and solitons.Comment: 12 pages, 14 figure
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