27 research outputs found
Phantom Friedmann Cosmologies and Higher-Order Characteristics of Expansion
We discuss a more general class of phantom () cosmologies with
various forms of both phantom () matter. We
show that many types of evolution which include both Big-Bang and Big-Rip
singularities are admitted and give explicit examples. Among some interesting
models, there exist non-singular oscillating (or "bounce") cosmologies, which
appear due to a competition between positive and negative pressure of variety
of matter content. From the point of view of the current observations the most
interesting cosmologies are the ones which start with a Big-Bang and terminate
at a Big-Rip. A related consequence of having a possibility of two types of
singularities is that there exists an unstable static universe approached by
the two asymptotic models - one of them reaches Big-Bang, and another reaches
Big-Rip. We also give explicit relations between density parameters
and the dynamical characteristics for these generalized phantom models,
including higher-order observational characteristics such as jerk and "kerk".
Finally, we discuss the observational quantities such as luminosity distance,
angular diameter, and source counts, both in series expansion and explicitly,
for phantom models. Our series expansion formulas for the luminosity distance
and the apparent magnitude go as far as to the fourth-order in redshift
term, which includes explicitly not only the jerk, but also the "kerk" (or
"snap") which may serve as an indicator of the curvature of the universe.Comment: REVTEX 4, 23 pages, references updated, to appear in Annals of
Physics (N.Y.
Geometry of Quantum Spheres
Spectral triples on the q-deformed spheres of dimension two and three are
reviewed.Comment: 23 pages, revie
Quantum spin coverings and statistics
SL_q(2) at odd roots of unity q^l =1 is studied as a quantum cover of the
complex rotation group SO(3,C), in terms of the associated Hopf algebras of
(quantum) polynomial functions. We work out the irreducible corepresentations,
the decomposition of their tensor products and a coquasitriangular structure,
with the associated braiding (or statistics). As an example, the case l=3 is
discussed in detail.Comment: 15 page
Supersymmetries of the spin-1/2 particle in the field of magnetic vortex, and anyons
The quantum nonrelativistic spin-1/2 planar systems in the presence of a
perpendicular magnetic field are known to possess the N=2 supersymmetry. We
consider such a system in the field of a magnetic vortex, and find that there
are just two self-adjoint extensions of the Hamiltonian that are compatible
with the standard N=2 supersymmetry. We show that only in these two cases one
of the subsystems coincides with the original spinless Aharonov-Bohm model and
comes accompanied by the super-partner Hamiltonian which allows a singular
behavior of the wave functions. We find a family of additional, nonlocal
integrals of motion and treat them together with local supercharges in the
unifying framework of the tri-supersymmetry. The inclusion of the dynamical
conformal symmetries leads to an infinitely generated superalgebra, that
contains several representations of the superconformal osp(2|2) symmetry. We
present the application of the results in the framework of the two-body model
of identical anyons. The nontrivial contact interaction and the emerging N=2
linear and nonlinear supersymmetries of the anyons are discussed.Comment: 18 pages, 1 figure, published versio