6,136 research outputs found
Supersymmetry of the magnetic vortex
The N=2 supersymmetry of the Pauli Hamiltonian in any static magnetic field
in the plane combines, for the magnetic vortex, with Jackiw's bosonic
symmetry, into an dynamical
supersymmetry.Comment: 4 pages. Originally Tours Preprint no 60/93 (1993). Unpublishe
On Maximal Unbordered Factors
Given a string of length , its maximal unbordered factor is the
longest factor which does not have a border. In this work we investigate the
relationship between and the length of the maximal unbordered factor of
. We prove that for the alphabet of size the expected length
of the maximal unbordered factor of a string of length~ is at least
(for sufficiently large values of ). As an application of this result, we
propose a new algorithm for computing the maximal unbordered factor of a
string.Comment: Accepted to the 26th Annual Symposium on Combinatorial Pattern
Matching (CPM 2015
Chiral fermions as classical massless spinning particles
Semiclassical chiral fermion models with Berry term are studied in a
symplectic framework. In the free case, the system can be obtained from
Souriau's model for a relativistic massless spinning particle by "enslaving"
the spin. The Berry term is identified with the classical spin two-form of the
latter model. The Souriau model carries a natural Poincar\'e symmetry that we
highlight, but spin enslavement breaks the boost symmetry. However the relation
between the models allows us to derive a Poincare symmetry of unconventional
form for chiral fermions. Then we couple our system to an external
electromagnetic field. For gyromagnetic ratio we get curious superluminal
Hall-type motions; for and in a pure constant magnetic field in
particular, we find instead spiraling motions.Comment: Substantially revised and extended version. 31 pages, 5 figures.
Details clarified and references added. To be published in PR
Anyons with anomalous gyromagnetic ratio & the Hall effect
Letting the mass depend on the spin-field coupling as
, we propose a new set of
relativistic planar equations of motion for spinning anyons. Our model can
accommodate any gyromagnetic ratio and provides us with a novel version of
the Bargmann-Michel-Telegdi equations in 2+1 dimensions. The system becomes
singular when the field takes a critical value, and, for , the only
allowed motions are those which satisfy the Hall law. For each a
secondary Hall effect arises also for another critical value of the field. The
non-relativistic limit of our equations yields new models which generalize our
previous ``exotic'' model, associated with the two-fold central extension of
the planar Galilei group.Comment: The affiliation of the first author's Institution is presented in
detail. LaTeX, 12 pages no figures. To appear in Phys. Lett.
Semidirect products and the Pukanszky condition
We study the general geometrical structure of the coadjoint orbits of a
semidirect product formed by a Lie group and a representation of this group on
a vector space. The use of symplectic induction methods gives new insight into
the structure of these orbits. In fact, each coadjoint orbit of such a group is
obtained by symplectic induction on some coadjoint orbit of a "smaller" Lie
group. We study also a special class of polarizations related to a semidirect
product and the validity of Pukanszky's condition for these polarizations. Some
examples of physical interest are discussed using the previous methods.Comment: 33 pages, including special macros and fonts (JGPpaper.tex is the
source TeX file), to appear in J. Geom. Phys., also available via anonymous
ftp or via gopher gopher://cpt.univ-mrs.fr
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