3,418 research outputs found
Bicrossproduct structure of the null-plane quantum Poincare algebra
A nonlinear change of basis allows to show that the non-standard quantum
deformation of the (3+1) Poincare algebra has a bicrossproduct structure.
Quantum universal R-matrix, Pauli-Lubanski and mass operators are presented in
the new basis.Comment: 7 pages, LaTe
Towards Spinfoam Cosmology
We compute the transition amplitude between coherent quantum-states of
geometry peaked on homogeneous isotropic metrics. We use the holomorphic
representations of loop quantum gravity and the
Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at
first order in the vertex expansion, second order in the graph (multipole)
expansion, and first order in 1/volume. We show that the resulting amplitude is
in the kernel of a differential operator whose classical limit is the canonical
hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an
indication that the dynamics of loop quantum gravity defined by the new vertex
yields the Friedmann equation in the appropriate limit.Comment: 8 page
Almost commutative Riemannian geometry: wave operators
Associated to any (pseudo)-Riemannian manifold of dimension is an
-dimensional noncommutative differential structure (\Omega^1,\extd) on
the manifold, with the extra dimension encoding the classical Laplacian as a
noncommutative `vector field'. We use the classical connection, Ricci tensor
and Hodge Laplacian to construct (\Omega^2,\extd) and a natural
noncommutative torsion free connection on . We show
that its generalised braiding \sigma:\Omega^1\tens\Omega^1\to
\Omega^1\tens\Omega^1 obeys the quantum Yang-Baxter or braid relations only
when the original is flat, i.e their failure is governed by the Riemann
curvature, and that \sigma^2=\id only when is Einstein. We show that if
has a conformal Killing vector field then the cross product algebra
viewed as a noncommutative analogue of has a
natural -dimensional calculus extending and a natural spacetime
Laplacian now directly defined by the extra dimension. The case
recovers the Majid-Ruegg bicrossproduct flat spacetime model and the
wave-operator used in its variable speed of light preduction, but now as an
example of a general construction. As an application we construct the wave
operator on a noncommutative Schwarzschild black hole and take a first look at
its features. It appears that the infinite classical redshift/time dilation
factor at the event horizon is made finite.Comment: 39 pages, 4 pdf images. Removed previous Sections 5.1-5.2 to a
separate paper (now ArXived) to meet referee length requirements.
Corresponding slight restructure but no change to remaining conten
Quantum Deformations of Space-Time Symmetries with Mass-Like Deformation Parameter
The difficulties with the measurability of classical space-time distances are
considered. We outline the framework of quantum deformations of D=4 space-time
symmetries with dimensionfull deformation parameter, and present some recent
results.Comment: 4 pages, LaTeX, uses file stwol.sty, to be published in the
Proceedings of XXXII International Rochester Conference in High Energy
Physics (Warsaw, 24.07-31.07 1996
Braided Matrix Structure of the Sklyanin Algebra and of the Quantum Lorentz Group
Braided groups and braided matrices are novel algebraic structures living in
braided or quasitensor categories. As such they are a generalization of
super-groups and super-matrices to the case of braid statistics. Here we
construct braided group versions of the standard quantum groups . They
have the same FRT generators but a matrix braided-coproduct \und\Delta
L=L\und\tens L where , and are self-dual. As an application, the
degenerate Sklyanin algebra is shown to be isomorphic to the braided matrices
; it is a braided-commutative bialgebra in a braided category. As a
second application, we show that the quantum double D(\usl) (also known as
the `quantum Lorentz group') is the semidirect product as an algebra of two
copies of \usl, and also a semidirect product as a coalgebra if we use braid
statistics. We find various results of this type for the doubles of general
quantum groups and their semi-classical limits as doubles of the Lie algebras
of Poisson Lie groups.Comment: 45 pages. Revised (= much expanded introduction
Braided structure of fractional -supersymmetry
It is shown that fractional -superspace is isomorphic to the
limit of the braided line. -supersymmetry is
identified as translational invariance along this line. The fractional
translation generator and its associated covariant derivative emerge as the
limits of the left and right derivatives from the calculus
on the braided lineComment: 8 pages, LaTeX, submitted to Proceedings of the 5th Colloquium
`Quantum groups and integrable systems', Prague, June 1996 (to appear in
Czech. J. Phys.
An Efficient Automatic Mass Classification Method In Digitized Mammograms Using Artificial Neural Network
In this paper we present an efficient computer aided mass classification
method in digitized mammograms using Artificial Neural Network (ANN), which
performs benign-malignant classification on region of interest (ROI) that
contains mass. One of the major mammographic characteristics for mass
classification is texture. ANN exploits this important factor to classify the
mass into benign or malignant. The statistical textural features used in
characterizing the masses are mean, standard deviation, entropy, skewness,
kurtosis and uniformity. The main aim of the method is to increase the
effectiveness and efficiency of the classification process in an objective
manner to reduce the numbers of false-positive of malignancies. Three layers
artificial neural network (ANN) with seven features was proposed for
classifying the marked regions into benign and malignant and 90.91% sensitivity
and 83.87% specificity is achieved that is very much promising compare to the
radiologist's sensitivity 75%.Comment: 13 pages, 10 figure
Noncommutative Harmonic Analysis, Sampling Theory and the Duflo Map in 2+1 Quantum Gravity
We show that the -product for , group Fourier transform and
effective action arising in [1] in an effective theory for the integer spin
Ponzano-Regge quantum gravity model are compatible with the noncommutative
bicovariant differential calculus, quantum group Fourier transform and
noncommutative scalar field theory previously proposed for 2+1 Euclidean
quantum gravity using quantum group methods in [2]. The two are related by a
classicalisation map which we introduce. We show, however, that noncommutative
spacetime has a richer structure which already sees the half-integer spin
information. We argue that the anomalous extra `time' dimension seen in the
noncommutative geometry should be viewed as the renormalisation group flow
visible in the coarse-graining in going from to . Combining our
methods we develop practical tools for noncommutative harmonic analysis for the
model including radial quantum delta-functions and Gaussians, the Duflo map and
elements of `noncommutative sampling theory'. This allows us to understand the
bandwidth limitation in 2+1 quantum gravity arising from the bounded
momentum and to interpret the Duflo map as noncommutative compression. Our
methods also provide a generalised twist operator for the -product.Comment: 53 pages latex, no figures; extended the intro for this final versio
Waves on Noncommutative Spacetime and Gamma-Ray Bursts
Quantum group Fourier transform methods are applied to the study of processes
on noncommutative Minkowski spacetime . A natural
wave equation is derived and the associated phenomena of {\it in vacuo}
dispersion are discussed. Assuming the deformation scale is of the
order of the Planck length one finds that the dispersion effects are large
enough to be tested in experimental investigations of astrophysical phenomena
such as gamma-ray bursts. We also outline a new approach to the construction of
field theories on the noncommutative spacetime, with the noncommutativity
equivalent under Fourier transform to non-Abelianness of the `addition law' for
momentum in Feynman diagrams. We argue that CPT violation effects of the type
testable using the sensitive neutral-kaon system are to be expected in such a
theory.Comment: 25 page
Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta
A noncommutative geometric generalisation of the quantum field theoretical
framework is developed by generalising the Heisenberg commutation relations.
There appear nonzero minimal uncertainties in positions and in momenta. As the
main result it is shown with the example of a quadratically ultraviolet
divergent graph in theory that nonzero minimal uncertainties in
positions do have the power to regularise. These studies are motivated with the
ansatz that nonzero minimal uncertainties in positions and in momenta arise
from gravity. Algebraic techniques are used that have been developed in the
field of quantum groups.Comment: 52 pages LATEX, DAMTP/93-33. Revised version now includes a chapter
on the Poincare algebra and curvature as noncommutativity of momentum spac
- …