18 research outputs found
Linear Connections on the Two Parameter Quantum Plane
We apply a recently proposed definition of a linear connection in non
commutative geometry based on the natural bimodule structure of the algebra of
differential forms to the case of the two-parameter quantum plane. We find that
there exists a non trivial family of linear connections only when the two
parameters obeys a specific relation.Comment: 7 pages, Te
Anyonic Excitations in Fast Rotating Bose Gases Revisited
The role of anyonic excitations in fast rotating harmonically trapped Bose
gases in a fractional Quantum Hall state is examined. Standard Chern-Simons
anyons as well as "non standard" anyons obtained from a statistical interaction
having Maxwell-Chern-Simons dynamics and suitable non minimal coupling to
matter are considered. Their respective ability to stabilize attractive Bose
gases under fast rotation in the thermodynamical limit is studied. Stability
can be obtained for standard anyons while for non standard anyons, stability
requires that the range of the corresponding statistical interaction does not
exceed the typical wavelenght of the atoms.Comment: 5 pages. Improved version to be published in Phys. Rev. A, including
a physical discussion on relevant interactions and scattering regime together
with implication on the nature of statistical interactio
Examples of derivation-based differential calculi related to noncommutative gauge theories
Some derivation-based differential calculi which have been used to construct
models of noncommutative gauge theories are presented and commented. Some
comparisons between them are made.Comment: 22 pages, conference given at the "International Workshop in honour
of Michel Dubois-Violette, Differential Geometry, Noncommutative Geometry,
Homology and Fundamental Interactions". To appear in a special issue of
International Journal of Geometric Methods in Modern Physic
Vortex in Maxwell-Chern-Simons models coupled to external backgrounds
We consider Maxwell-Chern-Simons models involving different non-minimal
coupling terms to a non relativistic massive scalar and further coupled to an
external uniform background charge. We study how these models can be
constrained to support static radially symmetric vortex configurations
saturating the lower bound for the energy. Models involving Zeeman-type
coupling support such vortices provided the potential has a "symmetry breaking"
form and a relation between parameters holds. In models where minimal coupling
is supplemented by magnetic and electric field dependant coupling terms, non
trivial vortex configurations minimizing the energy occur only when a non
linear potential is introduced. The corresponding vortices are studied
numericallyComment: LaTeX file, 2 figure
Quantum Hall Conductivity in a Landau Type Model with a Realistic Geometry
In this paper, we revisit some quantum mechanical aspects related to the
Quantum Hall Effect. We consider a Landau type model, paying a special
attention to the experimental and geometrical features of Quantum Hall
experiments. The resulting formalism is then used to compute explicitely the
Hall conductivity from a Kubo formula.Comment: LaTeX, 1 eps figur
Modular Groups, Visibility Diagram and Quantum Hall Effect
We consider the action of the modular group on the set of
positive rational fractions. From this, we derive a model for a classification
of fractional (as well as integer) Hall states which can be visualized on two
``visibility" diagrams, the first one being associated with even denominator
fractions whereas the second one is linked to odd denominator fractions. We use
this model to predict, among some interesting physical quantities, the relative
ratios of the width of the different transversal resistivity plateaus. A
numerical simulation of the tranversal resistivity plot based on this last
prediction fits well with the present experimental data.Comment: 17 pages, plain TeX, 4 eps figures included (macro epsf.tex), 1
figure available from reques
Noncommutative Induced Gauge Theories on Moyal Spaces
Noncommutative field theories on Moyal spaces can be conveniently handled
within a framework of noncommutative geometry. Several renormalisable matter
field theories that are now identified are briefly reviewed. The construction
of renormalisable gauge theories on these noncommutative Moyal spaces, which
remains so far a challenging problem, is then closely examined. The computation
in 4-D of the one-loop effective gauge theory generated from the integration
over a scalar field appearing in a renormalisable theory minimally coupled to
an external gauge potential is presented. The gauge invariant effective action
is found to involve, beyond the expected noncommutative version of the pure
Yang-Mills action, additional terms that may be interpreted as the gauge theory
counterpart of the harmonic term, which for the noncommutative -theory
on Moyal space ensures renormalisability. A class of possible candidates for
renormalisable gauge theory actions defined on Moyal space is presented and
discussed.Comment: 24 pages, 6 figures. Talk given at the "International Conference on
Noncommutative Geometry and Physics", April 2007, Orsay (France). References
updated. To appear in J. Phys. Conf. Se
Global quantum Hall phase diagram from visibility diagrams
We propose a construction of a global phase diagram for the quantum Hall
effect. This global phase diagram is based on our previous constructions of
visibility diagrams in the context of the Quantum Hall Effect. The topology of
the phase diagram we obtain is in good agreement with experimental observations
(when the spin effect can be neglected). This phase diagram does not show
floating.Comment: LaTeX2e, 9 pages, 5 eps figure
Symmetry breaking, conformal geometry and gauge invariance
When the electroweak action is rewritten in terms of SU(2) gauge invariant
variables, the Higgs can be interpreted as a conformal metric factor. We show
that asymptotic flatness of the metric is required to avoid a Gribov problem:
without it, the new variables fail to be nonperturbatively gauge invariant. We
also clarify the relations between this approach and unitary gauge fixing, and
the existence of similar transformations in other gauge theories.Comment: 11 pages. Version 2: typos corrected, discussion of Elitzur's theorem
added. Version to appear in J.Phys.