229 research outputs found
Non-commutative connections of the second kind
A connection-like objects, termed {\em hom-connections} are defined in the
realm of non-commutative geometry. The definition is based on the use of
homomorphisms rather than tensor products. It is shown that hom-connections
arise naturally from (strong) connections in non-commutative principal bundles.
The induction procedure of hom-connections via a map of differential graded
algebras or a differentiable bimodule is described. The curvature for a
hom-connection is defined, and it is shown that flat hom-connections give rise
to a chain complex.Comment: 13 pages, LaTe
Quantum teardrops
Algebras of functions on quantum weighted projective spaces are introduced,
and the structure of quantum weighted projective lines or quantum teardrops are
described in detail. In particular the presentation of the coordinate algebra
of the quantum teardrop in terms of generators and relations and classification
of irreducible *-representations are derived. The algebras are then analysed
from the point of view of Hopf-Galois theory or the theory of quantum principal
bundles. Fredholm modules and associated traces are constructed. C*-algebras of
continuous functions on quantum weighted projective lines are described and
their K-groups computed.Comment: 18 page
Aliens attack – population dynamics and density control of American mink Neovison vison in four National Parks in Poland
Niemczynowicz, A., Brzeziński, M., Zalewski, A
The Serre spectral sequence of a noncommutative fibration for de Rham cohomology
For differential calculi on noncommutative algebras, we construct a twisted
de Rham cohomology using flat connections on modules. This has properties
similar, in some respects, to sheaf cohomology on topological spaces. We also
discuss generalised mapping properties of these theories, and relations of
these properties to corings. Using this, we give conditions for the Serre
spectral sequence to hold for a noncommutative fibration. This might be better
read as giving the definition of a fibration in noncommutative differential
geometry. We also study the multiplicative structure of such spectral
sequences. Finally we show that some noncommutative homogeneous spaces satisfy
the conditions to be such a fibration, and in the process clarify the
differential structure on these homogeneous spaces. We also give two explicit
examples of differential fibrations: these are built on the quantum Hopf
fibration with two different differential structures.Comment: LaTeX, 33 page
Empiric Models of the Earth's Free Core Nutation
Free core nutation (FCN) is the main factor that limits the accuracy of the
modeling of the motion of Earth's rotational axis in the celestial coordinate
system. Several FCN models have been proposed. A comparative analysis is made
of the known models including the model proposed by the author. The use of the
FCN model is shown to substantially increase the accuracy of the modeling of
Earth's rotation. Furthermore, the FCN component extracted from the observed
motion of Earth's rotational axis is an important source for the study of the
shape and rotation of the Earth's core. A comparison of different FCN models
has shown that the proposed model is better than other models if used to
extract the geophysical signal (the amplitude and phase of FCN) from
observational data.Comment: 8 pages, 3 figures; minor update of the journal published versio
A Non-Associative Deformation of Yang-Mills Gauge Theory
An ansatz is presented for a possible non-associative deformation of the
standard Yang-Mills type gauge theories. An explicit algebraic structure for
the deformed gauge symmetry is put forward and the resulting gauge theory
developed. The non-associative deformation is constructed in such a way that an
apparently associative Lie algebraic structure is retained modulo a closure
problem for the generators. It is this failure to close which leads to new
physics in the model as manifest in the gauge field kinetic term in the
resulting Lagrangian. A possible connection between this model and quantum
group gauge theories is also investigated.Comment: 18 pages, RevTeX, also uses aps.st
Canonical quantization of a particle near a black hole
We discuss the quantization of a particle near an extreme Reissner-Nordstrom
black hole in the canonical formalism. This model appears to be described by a
Hamiltonian with no well-defined ground state. This problem can be circumvented
by a redefinition of the Hamiltonian due to de Alfaro, Fubini and Furlan (DFF).
We show that the Hamiltonian with no ground state corresponds to a gauge in
which there is an obstruction at the boundary of spacetime requiring a
modification of the quantization rules. The redefinition of the Hamiltonian a
la DFF corresponds to a different choice of gauge. The latter is a good gauge
leading to standard quantization rules. Thus, the DFF trick is a consequence of
a standard gauge-fixing procedure in the case of black hole scattering.Comment: 13 pages, ReVTeX, no figure
Direct measurement of diurnal polar motion by ring laser gyroscopes
We report the first direct measurements of the very small effect of forced
diurnal polar motion, successfully observed on three of our large ring lasers,
which now measure the instantaneous direction of Earth's rotation axis to a
precision of 1 part in 10^8 when averaged over a time interval of several
hours. Ring laser gyroscopes provide a new viable technique for directly and
continuously measuring the position of the instantaneous rotation axis of the
Earth and the amplitudes of the Oppolzer modes. In contrast, the space geodetic
techniques (VLBI, SLR, GPS, etc.) contain no information about the position of
the instantaneous axis of rotation of the Earth, but are sensitive to the
complete transformation matrix between the Earth-fixed and inertial reference
frame. Further improvements of gyroscopes will provide a powerful new tool for
studying the Earth's interior.Comment: 5 pages, 4 figures, agu2001.cl
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