1,438 research outputs found
Scaling Identities for Solitons beyond Derrick's Theorem
New integral identities satisfied by topological solitons in a range of
classical field theories are presented. They are derived by considering
independent length rescalings in orthogonal directions, or equivalently, from
the conservation of the stress tensor. These identities are refinements of
Derrick's theorem.Comment: 10 page
Deconstructing Supersymmetry
Two supersymmetric classical mechanical systems are discussed. Concrete
realizations are obtained by supposing that the dynamical variables take values
in a Grassmann algebra with two generators. The equations of motion are
explicitly solved.Comment: 19 pages, Tex fil
Light Nuclei as Quantized Skyrmions
We consider the rigid body quantization of Skyrmions with topological charges
1 to 8, as approximated by the rational map ansatz. Novel, general expressions
for the elements of the inertia tensors, in terms of the approximating rational
map, are presented and are used to determine the kinetic energy contribution to
the total energy of the ground and excited states of the quantized Skyrmions.
Our results are compared to the experimentally determined energy levels of the
corresponding nuclei, and the energies and spins of a few as yet unobserved
states are predicted.Comment: 33 pages, 16 figures, Section 13 replace
Thermodynamics of Vortices in the Plane
The thermodynamics of vortices in the critically coupled abelian Higgs model,
defined on the plane, are investigated by placing vortices in a region of
the plane with periodic boundary conditions: a torus. It is noted that the
moduli space for vortices, which is the same as that of
indistinguishable points on a torus, fibrates into a bundle over the
Jacobi manifold of the torus. The volume of the moduli space is a product of
the area of the base of this bundle and the volume of the fibre. These two
values are determined by considering two 2-surfaces in the bundle corresponding
to a rigid motion of a vortex configuration, and a motion around a fixed centre
of mass. The partition function for the vortices is proportional to the volume
of the moduli space, and the equation of state for the vortices is in the thermodynamic limit, where is the pressure, the area of
the region of the plane occupied by the vortices, and the temperature.
There is no phase transition.Comment: 17 pages, DAMTP 93-3
The interaction energy of well-separated Skyrme solitons
We prove that the asymptotic field of a Skyrme soliton of any degree has a
non-trivial multipole expansion. It follows that every Skyrme soliton has a
well-defined leading multipole moment. We derive an expression for the linear
interaction energy of well-separated Skyrme solitons in terms of their leading
multipole moments. This expression can always be made negative by suitable
rotations of one of the Skyrme solitons in space and iso-space.We show that the
linear interaction energy dominates for large separation if the orders of the
Skyrme solitons' multipole moments differ by at most two. In that case there
are therefore always attractive forces between the Skyrme solitons.Comment: 27 pages amslate
Solitons in a Baby-Skyrme model with invariance under area preserving diffeomorphisms
We study the properties of soliton solutions in an analog of the Skyrme model
in 2+1 dimensions whose Lagrangian contains the Skyrme term and the mass term,
but no usual kinetic term. The model admits a symmetry under area preserving
diffeomorphisms. We solve the dynamical equations of motion analytically for
the case of spinning isolated baryon type solitons. We take fully into account
the induced deformation of the spinning Skyrmions and the consequent
modification of its moment of inertia to give an analytical example of related
numerical behaviour found by Piette et al.. We solve the equations of motion
also for the case of an infinite, open string, and a closed annular string. In
each case, the solitons are of finite extent, so called "compactons", being
exactly the vacuum outside a compact region. We end with indications on the
scattering of baby-Skyrmions, as well as some considerations as the properties
of solitons on a curved space.Comment: 30 pages, 5 figures, revtex, major modifications, conclusions
modifie
Angularly localized Skyrmions
Quantized Skyrmions with baryon numbers and 4 are considered and
angularly localized wavefunctions for them are found. By combining a few low
angular momentum states, one can construct a quantum state whose spatial
density is close to that of the classical Skyrmion, and has the same
symmetries. For the B=1 case we find the best localized wavefunction among
linear combinations of and angular momentum states. For B=2, we
find that the ground state has toroidal symmetry and a somewhat reduced
localization compared to the classical solution. For B=4, where the classical
Skyrmion has cubic symmetry, we construct cubically symmetric quantum states by
combining the ground state with the lowest rotationally excited
state. We use the rational map approximation to compare the classical and
quantum baryon densities in the B=2 and B=4 cases.Comment: 22 page
Reparametrising the Skyrme Model using the Lithium-6 Nucleus
The minimal energy B=6 solution of the Skyrme model is a static soliton with
symmetry. The symmetries of the solution imply that the quantum
numbers of the ground state are the same as those of the Lithium-6 nucleus.
This identification is considered further by obtaining expressions for the mean
charge radius and quadrupole moment, dependent only on the Skyrme model
parameters (a dimensionless constant) and (the pion decay
constant). The optimal values of these parameters have often been deliberated
upon, and we propose, for , changing them from those which are most
commonly accepted. We obtain specific values for these parameters for B=6, by
matching with properties of the Lithium-6 nucleus. We find further support for
the new values by reconsidering the -particle and deuteron as quantized
B=4 and B=2 Skyrmions.Comment: 18 page
Kink dynamics in a novel discrete sine-Gordon system
A spatially-discrete sine-Gordon system with some novel features is
described. There is a topological or Bogomol'nyi lower bound on the energy of a
kink, and an explicit static kink which saturates this bound. There is no
Peierls potential barrier, and consequently the motion of a kink is simpler,
especially at low speeds. At higher speeds, it radiates and slows down.Comment: 10 pages, 7 figures, archivin
Electrically Charged Sphalerons
We investigate the possibility that the Higgs sector of the Weinberg-Salam
model admits the existence of electrically charged, sphaleron states. Evidence
is provided through an asymptotic and numerical perturbative analysis about the
uncharged sphaleron. By introducing a toy model in two dimensions we
demonstrate that such electrically charged, unstable states can exist.
Crucially, they can have a comparable mass to their uncharged counterparts and
so may also play a role in electroweak baryogenesis, by opening up new channels
for baryon number violating processes.Comment: 12 pages, 4 Postscript figure
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