216 research outputs found
Mixmaster Horava-Witten Cosmology
We discuss various superstring effective actions and, in particular, their
common sector which leads to the so-called pre-big-bang cosmology (cosmology in
a weak coupling limit of heterotic superstring). Then, we review the main ideas
of the Horava-Witten theory which is a strong coupling limit of heterotic
superstring theory. Using the conformal relationship between these two theories
we present Kasner asymptotic solutions of Bianchi type IX geometries within
these theories and make predictions about possible emergence of chaos. Finally,
we present a possible method of generating Horava-Witten cosmological solutions
out of the well-known general relativistic pre-big-bang solutions.Comment: 7 pages, 2 figures, based on the talks given at Marcel Grossmann
Meeting IX, Rome 2000 and at "Supersymmetry and Quantum Field Theory" (D.V.
Volkov Memorial), Kharkov 2000, espcrc2.sty include
Spacetime averaging of exotic singularity universes
Taking a spacetime average as a measure of the strength of singularities we
show that big-rips (type I) are stronger than big-bangs. The former have
infinite spacetime averages while the latter have them equal to zero. The
sudden future singularities (type II) and singularities (type V) have
finite spacetime averages. The finite scale factor (type III) singularities for
some values of the parameters may have an infinite average and in that sense
they may be considered stronger than big-bangs.Comment: 5 pages, no figures, REVTEX4-1, minor improvement
The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere
Equivariance under the action of Uq(so(5)) is used to compute the left
regular and (chiral) spinorial representations of the algebra of the orthogonal
quantum 4-sphere S^4_q. These representations are the constituents of a
spectral triple on this sphere with a Dirac operator which is isospectral to
the canonical one on the round undeformed four-sphere and which gives metric
dimension four for the noncommutative geometry. Non-triviality of the geometry
is proved by pairing the associated Fredholm module with an `instanton'
projection. We also introduce a real structure which satisfies all required
properties modulo smoothing operators.Comment: 40 pages, no figures, Latex. v2: Title changed. Sect. 9 on real
structure completely rewritten and results strengthened. Additional minor
changes throughout the pape
Inhomogenized sudden future singularities
We find that sudden future singularities may also appear in spatially
inhomogeneous Stephani models of the universe. They are temporal pressure
singularities and may appear independently of the spatial finite density
singularities already known to exist in these models. It is shown that the main
advantage of the homogeneous sudden future singularities which is the
fulfillment of the strong and weak energy conditions may not be the case for
inhomogeneous models.Comment: REVTEX 4, 5 pages, no figures, a discussion of the most general case
include
The Spectral Geometry of the Equatorial Podles Sphere
We propose a slight modification of the properties of a spectral geometry a
la Connes, which allows for some of the algebraic relations to be satisfied
only modulo compact operators. On the equatorial Podles sphere we construct
suq2-equivariant Dirac operator and real structure which satisfy these modified
properties.Comment: 6 pages. Latex. V2: Minor changes; to appear in Comptes Rendus
Mathematiqu
Simple Dynamics on the Brane
We apply methods of dynamical systems to study the behaviour of the
Randall-Sundrum models. We determine evolutionary paths for all possible
initial conditions in a 2-dimensional phase space and we investigate the set of
accelerated models. The simplicity of our formulation in comparison to some
earlier studies is expressed in the following: our dynamical system is a
2-dimensional Hamiltonian system, and what is more advantageous, it is free
from the degeneracy of critical points so that the system is structurally
stable. The phase plane analysis of Randall-Sundrum models with isotropic
Friedmann geometry clearly shows that qualitatively we deal with the same types
of evolution as in general relativity, although quantitatively there are
important differences.Comment: an improved version, 34 pages, 9 eps figure
Generalised boundary conditions for the Aharonov-Bohm effect combined with a homogeneous magnetic field
The most general admissible boundary conditions are derived for an idealised
Aharonov-Bohm flux intersecting the plane at the origin on the background of a
homogeneous magnetic field. A standard technique based on self-adjoint
extensions yields a four-parameter family of boundary conditions; other two
parameters of the model are the Aharonov-Bohm flux and the homogeneous magnetic
field. The generalised boundary conditions may be regarded as a combination of
the Aharonov-Bohm effect with a point interaction. Spectral properties of the
derived Hamiltonians are studied in detail.Comment: 32 pages, a LaTeX source file with 2 eps figures; submitted to J.
Math. Phy
Local Index Formula on the Equatorial Podles Sphere
We discuss spectral properties of the equatorial Podles sphere. As a
preparation we also study the `degenerate' (i.e. ) case (related to the
quantum disk). We consider two different spectral triples: one related to the
Fock representation of the Toeplitz algebra and the isopectral one. After the
identification of the smooth pre--algebra we compute the dimension
spectrum and residues. We check the nontriviality of the (noncommutative) Chern
character of the associated Fredholm modules by computing the pairing with the
fundamental projector of the -algebra (the nontrivial generator of the
-group) as well as the pairing with the -analogue of the Bott
projector. Finally, we show that the local index formula is trivially
satisfied.Comment: 18 pages, no figures; minor correction
Metrics and Pairs of Left and Right Connections on Bimodules
Properties of metrics and pairs consisting of left and right connections are
studied on the bimodules of differential 1-forms. Those bimodules are obtained
from the derivation based calculus of an algebra of matrix valued functions,
and an SL\sb q(2,\IC)-covariant calculus of the quantum plane plane at a
generic and the cubic root of unity. It is shown that, in the
aforementioned examples, giving up the middle-linearity of metrics
significantly enlarges the space of metrics. A~metric compatibility condition
for the pairs of left and right connections is defined. Also, a compatibility
condition between a left and right connection is discussed. Consequences
entailed by reducing to the centre of a bimodule the domain of those conditions
are investigated in detail. Alternative ways of relating left and right
connections are considered.Comment: 16 pages, LaTeX, nofigure
Aharonov-Bohm Effect with --type Interaction
A quantum particle interacting with a thin solenoid and a magnetic flux is
described by a five-parameter family of Hamilton operators, obtained via the
method of self-adjoint extensions. One of the parameters, the value of the
flux, corresponds to the Aharonov-Bohm effect; the other four parameters
correspond to the strength of a singular potential barrier. The spectrum and
eigenstates are computed and the scattering problem is solved.Comment: 19 pages, Late
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