282 research outputs found
Thermodynamic Properties of a Quantum Group Boson Gas
An approach is proposed enabling to effectively describe the behaviour of a
bosonic system. The approach uses the quantum group formalism. In
effect, considering a bosonic Hamiltonian in terms of the
generators, it is shown that its thermodynamic properties are connected to
deformation parameters and . For instance, the average number of
particles and the pressure have been computed. If is fixed to be the same
value for , our approach coincides perfectly with some results developed
recently in this subject. The ordinary results, of the present system, can be
found when we take the limit .Comment: 13 pages, Late
Differential Calculus on the Quantum Superspace and Deformation of Phase Space
We investigate non-commutative differential calculus on the supersymmetric
version of quantum space where the non-commuting super-coordinates consist of
bosonic as well as fermionic (Grassmann) coordinates. Multi-parametric quantum
deformation of the general linear supergroup, , is studied and the
explicit form for the -matrix, which is the solution of the
Yang-Baxter equation, is presented. We derive the quantum-matrix commutation
relation of and the quantum superdeterminant. We apply these
results for the to the deformed phase-space of supercoordinates and
their momenta, from which we construct the -matrix of q-deformed
orthosymplectic group and calculate its -matrix. Some
detailed argument for quantum super-Clifford algebras and the explict
expression of the -matrix will be presented for the case of
.Comment: 17 pages, KUCP-4
Quantum Deformed Algebra and Superconformal Algebra on Quantum Superspace
We study a deformed algebra on a quantum superspace. Some
interesting aspects of the deformed algebra are shown. As an application of the
deformed algebra we construct a deformed superconformal algebra. {}From the
deformed algebra, we derive deformed Lorentz, translation of
Minkowski space, and its supersymmetric algebras as closed
subalgebras with consistent automorphisms.Comment: 27 pages, KUCP-59, LaTeX fil
The exponential map for representations of
For the quantum group and the corresponding quantum algebra
Fronsdal and Galindo explicitly constructed the so-called
universal -matrix. In a previous paper we showed how this universal
-matrix can be used to exponentiate representations from the quantum algebra
to get representations (left comodules) for the quantum group. Here, further
properties of the universal -matrix are illustrated. In particular, it is
shown how to obtain comodules of the quantum algebra by exponentiating modules
of the quantum group. Also the relation with the universal -matrix is
discussed.Comment: LaTeX-file, 7 pages. Submitted for the Proceedings of the 4th
International Colloquium ``Quantum Groups and Integrable Systems,'' Prague,
22-24 June 199
On the Differential Geometry of
The differential calculus on the quantum supergroup GL was
introduced by Schmidke {\it et al}. (1990 {\it Z. Phys. C} {\bf 48} 249). We
construct a differential calculus on the quantum supergroup GL in a
different way and we obtain its quantum superalgebra. The main structures are
derived without an R-matrix. It is seen that the found results can be written
with help of a matrix Comment: 14 page
Lagrangian and Hamiltonian Formalism on a Quantum Plane
We examine the problem of defining Lagrangian and Hamiltonian mechanics for a
particle moving on a quantum plane . For Lagrangian mechanics, we
first define a tangent quantum plane spanned by noncommuting
particle coordinates and velocities. Using techniques similar to those of Wess
and Zumino, we construct two different differential calculi on .
These two differential calculi can in principle give rise to two different
particle dynamics, starting from a single Lagrangian. For Hamiltonian
mechanics, we define a phase space spanned by noncommuting
particle coordinates and momenta. The commutation relations for the momenta can
be determined only after knowing their functional dependence on coordinates and
velocities.
Thus these commutation relations, as well as the differential calculus on
, depend on the initial choice of Lagrangian. We obtain the
deformed Hamilton's equations of motion and the deformed Poisson brackets, and
their definitions also depend on our initial choice of Lagrangian. We
illustrate these ideas for two sample Lagrangians. The first system we examine
corresponds to that of a nonrelativistic particle in a scalar potential. The
other Lagrangian we consider is first order in time derivative
Estrogens regulate early embryonic development of the olfactory sensory system via estrogen-responsive glia.
This is the final version. Available from The Company of Biologists via the DOI in this record. Estrogens are well-known to regulate development of sexual dimorphism of the brain; however, their role in embryonic brain development prior to sex-differentiation is unclear. Using estrogen biosensor zebrafish models, we found that estrogen activity in the embryonic brain occurs from early neurogenesis specifically in a type of glia in the olfactory bulb (OB), which we name estrogen-responsive olfactory bulb (EROB) cells. In response to estrogen, EROB cells overlay the outermost layer of the OB and interact tightly with olfactory sensory neurons at the olfactory glomeruli. Inhibiting estrogen activity using an estrogen receptor antagonist, ICI182,780 (ICI), and/or EROB cell ablation impedes olfactory glomerular development, including the topological organisation of olfactory glomeruli and inhibitory synaptogenesis in the OB. Furthermore, activation of estrogen signalling inhibits both intrinsic and olfaction-dependent neuronal activity in the OB, whereas ICI or EROB cell ablation results in the opposite effect on neuronal excitability. Altering the estrogen signalling disrupts olfaction-mediated behaviour in later larval stage. We propose that estrogens act on glia to regulate development of OB circuits, thereby modulating the local excitability in the OB and olfaction-mediated behaviour.Biotechnology and Biological Sciences Research CouncilBiotechnology and Biological Sciences Research CouncilUniversity of Exete
Automorphisms of associative algebras and noncommutative geometry
A class of differential calculi is explored which is determined by a set of
automorphisms of the underlying associative algebra. Several examples are
presented. In particular, differential calculi on the quantum plane, the
-deformed plane and the quantum group GLpq(2) are recovered in this way.
Geometric structures like metrics and compatible linear connections are
introduced.Comment: 28 pages, some references added, several amendments of minor
importance, remark on modular group in section 8 omitted, to appear in J.
Phys.
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