24 research outputs found
Nonabelian Global Chiral Symmetry Realisation in the Two-Dimensional N Flavour Massless Schwinger Model
The nonabelian global chiral symmetries of the two-dimensional N flavour
massless Schwinger model are realised through bosonisation and a vertex
operator construction.Comment: To appear in the Proceedings of the Fourth International Workshop on
Contemporary Problems in Mathematical Physics, November 5-11, 2005, Cotonou
(Republic of Benin) (World Scientific, Singapore, 2006), 1+7 pages, no
figure
Bosonization of the Schwinger Model by Noncommutative Chiral Bosons
Bosonization of the Schwinger model with noncommutative chiral bosons is
considered on a spacetime of cylinder topology. Using point splitting
regularization, manifest gauge invariance is maintained throughout. Physical
consequences are discussed.Comment: To appear in the Proceedings of the Fourth International Workshop on
Contemporary Problems in Mathematical Physics, November 5-11, 2005, Cotonou
(Republic of Benin) (World Scientific, Singapore, 2006), 1+8 pages, no
figure
Supersymmetric Quantum Mechanics, Engineered Hierarchies of Integrable Potentials, and the Generalised Laguerre Polynomials
Within the context of Supersymmetric Quantum Mechanics and its related
hierarchies of integrable quantum Hamiltonians and potentials, a general
programme is outlined and applied to its first two simplest illustrations.
Going beyond the usual restriction of shape invariance for intertwined
potentials, it is suggested to require a similar relation for Hamiltonians in
the hierarchy separated by an arbitrary number of levels, N. By requiring
further that these two Hamiltonians be in fact identical up to an overall shift
in energy, a periodic structure is installed in the hierarchy of quantum
systems which should allow for its solution. Specific classes of orthogonal
polynomials characteristic of such periodic hierarchies are thereby generated,
while the methods of Supersymmetric Quantum Mechanics then lead to generalised
Rodrigues formulae and recursion relations for such polynomials. The approach
also offers the practical prospect of quantum modelling through the engineering
of quantum potentials from experimental energy spectra. In this paper these
ideas are presented and solved explicitly for the cases N=1 and N=2. The latter
case is related to the generalised Laguerre polynomials, for which indeed new
results are thereby obtained. At the same time new classes of integrable
quantum potentials which generalise that of the harmonic oscillator and which
are characterised by two arbitrary energy gaps are identified, for which a
complete solution is achieved algebraically.Comment: 1+19 page
(p,q)-Deformations and (p,q)-Vector Coherent States of the Jaynes-Cummings Model in the Rotating Wave Approximation
Classes of (p,q)-deformations of the Jaynes-Cummings model in the rotating
wave approximation are considered. Diagonalization of the Hamiltonian is
performed exactly, leading to useful spectral decompositions of a series of
relevant operators. The latter include ladder operators acting between adjacent
energy eigenstates within two separate infinite discrete towers, except for a
singleton state. These ladder operators allow for the construction of
(p,q)-deformed vector coherent states. Using (p,q)-arithmetics, explicit and
exact solutions to the associated moment problem are displayed, providing new
classes of coherent states for such models. Finally, in the limit of decoupled
spin sectors, our analysis translates into (p,q)-deformations of the
supersymmetric harmonic oscillator, such that the two supersymmetric sectors
get intertwined through the action of the ladder operators as well as in the
associated coherent states.Comment: 1+25 pages, no figure
Variations on the Planar Landau Problem: Canonical Transformations, A Purely Linear Potential and the Half-Plane
The ordinary Landau problem of a charged particle in a plane subjected to a
perpendicular homogeneous and static magnetic field is reconsidered from
different points of view. The role of phase space canonical transformations and
their relation to a choice of gauge in the solution of the problem is
addressed. The Landau problem is then extended to different contexts, in
particular the singular situation of a purely linear potential term being added
as an interaction, for which a complete purely algebraic solution is presented.
This solution is then exploited to solve this same singular Landau problem in
the half-plane, with as motivation the potential relevance of such a geometry
for quantum Hall measurements in the presence of an electric field or a
gravitational quantum well
Modeling the Influence of Local Environmental Factors on Malaria Transmission in Benin and Its Implications for Cohort Study
Malaria remains endemic in tropical areas, especially in Africa. For the evaluation of new tools and to further our understanding of host-parasite interactions, knowing the environmental risk of transmission—even at a very local scale—is essential. The aim of this study was to assess how malaria transmission is influenced and can be predicted by local climatic and environmental factors