325 research outputs found
Conservation Laws in a First Order Dynamical System of Vortices
Gauge invariant conservation laws for the linear and angular momenta are
studied in a certain 2+1 dimensional first order dynamical model of vortices in
superconductivity. In analogy with fluid vortices it is possible to express the
linear and angular momenta as low moments of vorticity. The conservation laws
are compared with those obtained in the moduli space approximation for vortex
dynamics.Comment: LaTex file, 16 page
Static intervortex forces
A point particle approximation to the classical dynamics of well separated
vortices of the abelian Higgs model is developed. A static vortex is
asymptotically identical to a solution of the linearized field theory (a
Klein-Gordon/Proca theory) in the presence of a singular point source at the
vortex centre. It is shown that this source is a composite scalar monopole and
magnetic dipole, and the respective charges are determined numerically for
various values of the coupling constant. The interaction potential of two well
separated vortices is computed by calculating the interaction Lagrangian of two
such point sources in the linear theory. The potential is used to model type II
vortex scattering.Comment: Much shorter (10 pages) published version, new titl
Low Energy Skyrmion-Skyrmion Scattering
We study the scattering of Skyrmions at low energy and large separation using
the method proposed by Manton of truncation to a finite number of degrees
freedom. We calculate the induced metric on the manifold of the union of
gradient flow curves, which for large separation, to first non-trivial order is
parametrized by the variables of the product ansatz. (presented at the Lake
Louise Winter Institute, 1994)Comment: 6 page
Vortex Dynamics in Selfdual Maxwell-Higgs Systems with Uniform Background Electric Charge Density
We introduce selfdual Maxwell-Higgs systems with uniform background electric
charge density and show that the selfdual equations satisfied by topological
vortices can be reduced to the original Bogomol'nyi equations without any
background. These vortices are shown to carry no spin but to feel the Magnus
force due to the shielding charge carried by the Higgs field. We also study the
dynamics of slowly moving vortices and show that the spin-statistics theorem
holds to our vortices.Comment: 24 pages + 2 figures ( not included), Cu-TP-611, IASSNS-HEP-93/33,
NSF-ITP-93-13
Hypersurface Bohm-Dirac models
We define a class of Lorentz invariant Bohmian quantum models for N entangled
but noninteracting Dirac particles. Lorentz invariance is achieved for these
models through the incorporation of an additional dynamical space-time
structure provided by a foliation of space-time. These models can be regarded
as the extension of Bohm's model for N Dirac particles, corresponding to the
foliation into the equal-time hyperplanes for a distinguished Lorentz frame, to
more general foliations. As with Bohm's model, there exists for these models an
equivariant measure on the leaves of the foliation. This makes possible a
simple statistical analysis of position correlations analogous to the
equilibrium analysis for (the nonrelativistic) Bohmian mechanics.Comment: 17 pages, 3 figures, RevTex. Completely revised versio
Slow Schroedinger dynamics of gauged vortices
Multivortex dynamics in Manton's Schroedinger--Chern--Simons variant of the
Landau-Ginzburg model of thin superconductors is studied within a moduli space
approximation. It is shown that the reduced flow on M_N, the N vortex moduli
space, is hamiltonian with respect to \omega_{L^2}, the L^2 Kaehler form on
\M_N. A purely hamiltonian discussion of the conserved momenta associated with
the euclidean symmetry of the model is given, and it is shown that the
euclidean action on (M_N,\omega_{L^2}) is not hamiltonian. It is argued that
the N=3 flow is integrable in the sense of Liouville. Asymptotic formulae for
\omega_{L^2} and the reduced Hamiltonian for large intervortex separation are
conjectured. Using these, a qualitative analysis of internal 3-vortex dynamics
is given and a spectral stability analysis of certain rotating vortex polygons
is performed. Comparison is made with the dynamics of classical fluid point
vortices and geostrophic vortices.Comment: 22 pages, 2 figure
Simulating causal collapse models
We present simulations of causal dynamical collapse models of field theories
on a 1+1 null lattice. We use our simulations to compare and contrast two
possible interpretations of the models, one in which the field values are real
and the other in which the state vector is real. We suggest that a procedure of
coarse graining and renormalising the fundamental field can overcome its
noisiness and argue that this coarse grained renormalised field will show
interesting structure if the state vector does on the coarse grained scale.Comment: 18 pages, 8 fugures, LaTeX, Reference added, discussion of
probability distribution of labellings correcte
Reconnection of Non-Abelian Cosmic Strings
Cosmic strings in non-abelian gauge theories naturally gain a spectrum of
massless, or light, excitations arising from their embedding in color and
flavor space. This opens up the possibility that colliding strings miss each
other in the internal space, reducing the probability of reconnection. We study
the topology of the non-abelian vortex moduli space to determine the outcome of
string collision. Surprisingly we find that the probability of classical
reconnection in this system remains unity, with strings passing through each
other only for finely tuned initial conditions. We proceed to show how this
conclusion can be changed by symmetry breaking effects, or by quantum effects
associated to fermionic zero modes, and present examples where the probability
of reconnection in a U(N) gauge theory ranges from 1/N for low-energy
collisions to one at higher energies.Comment: 25 Pages, 3 Figures. v2: comment added, reference adde
NS5-Branes, T-Duality and Worldsheet Instantons
The equivalence of NS5-branes and ALF spaces under T-duality is well known.
However, a naive application of T-duality transforms the ALF space into a
smeared NS5-brane, de-localized on the dual, transverse, circle. In this paper
we re-examine this duality, starting from a two-dimensional N=(4,4) gauged
linear sigma model describing Taub-NUT space. After dualizing the circle fiber,
we find that the smeared NS5-brane target space metric receives corrections
from multi-worldsheet instantons. These instantons are identified as
Nielsen-Olesen vortices. We show that their effect is to break the isometry of
the target space, localizing the NS5-brane at a point. The contribution from
the k-instanton sector is shown to be proportional to the weighted integral of
the Euler form over the k-vortex moduli space. The duality also predicts the,
previously unknown, asymptotic exponential decay coefficient of the BPS vortex
solution.Comment: 26 pages. v2: Fourier modes of multi-vortex fermion zero mode
corrected. Reference added. v3: typo correcte
Vortex Dynamics in Self-Dual Chern-Simons Higgs Systems
We consider vortex dynamics in self-dual Chern-Simons Higgs systems. We show
that the naive Aharanov-Bohm phase is the inverse of the statistical phase
expected from the vortex spin, and that the self-dual configurations of
vortices are degenerate in energy but not in angular momentum. We also use the
path integral formalism to derive the dual formulation of Chern-Simons Higgs
systems in which vortices appear as charged particles. We argue that besides
the electromagnetic interaction, there is an additional interaction between
vortices, the so-called Magnus force, and that these forces can be put together
into a single `dual electromagnetic' interaction. This dual electromagnetic
interaction leads to the right Aharanov-Bohm phase. We also derive and study
the effective action for slowly moving vortices, which contains terms both
linear and quadratic in the vortex velocity.Comment: 36 pages and three figures (available under request), Columbia and
CERN preprin
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