36,609 research outputs found
Field theories on spaces with linear fuzziness
A noncommutative space is considered the position operators of which satisfy
the commutativity relations of a Lie algebra. The basic tools for calculation
on this space, including the product of the fields, inner product and the
proper measure for integration are derived. Some general aspects of
perturbative field theory calculations on this space are also discussed. Among
the features of such models is that they are free from ultraviolet divergences
(and hence free from UV/IR mixing as well), if the group is compact. The
example of the group SO(3) or SU(2) is investigated in more detail.Comment: 12 pages, no figs., LaTeX. v2: Comments and discussions are added,
e.g. on absence of UV/IR phenomena. No change in result
Quantum Mechanics as a Framework for Dealing with Uncertainty
Quantum uncertainty is described here in two guises: indeterminacy with its
concomitant indeterminism of measurement outcomes, and fuzziness, or
unsharpness. Both features were long seen as obstructions of experimental
possibilities that were available in the realm of classical physics. The birth
of quantum information science was due to the realization that such
obstructions can be turned into powerful resources. Here we review how the
utilization of quantum fuzziness makes room for a notion of approximate joint
measurement of noncommuting observables. We also show how from a classical
perspective quantum uncertainty is due to a limitation of measurability
reflected in a fuzzy event structure -- all quantum events are fundamentally
unsharp.Comment: Plenary Lecture, Central European Workshop on Quantum Optics, Turku
2009
Automatic histogram threshold using fuzzy measures
In this paper, an automatic histogram threshold approach based on a fuzziness measure is presented. This work is an improvement of an existing method. Using fuzzy logic concepts, the problems involved in finding the minimum of a criterion function are avoided. Similarity between gray levels is the key to find an optimal threshold. Two initial regions of gray levels, located at the boundaries of the histogram, are defined. Then, using an index of fuzziness, a similarity process is started to find the threshold point. A significant contrast between objects and background is assumed. Previous histogram equalization is used in small contrast images. No prior knowledge of the image is required.info:eu-repo/semantics/publishedVersio
Poisson structure on a space with linear SU(2) fuzziness
The Poisson structure is constructed for a model in which spatial coordinates
of configuration space are noncommutative and satisfy the commutation relations
of a Lie algebra. The case is specialized to that of the group SU(2), for which
the counterpart of the angular momentum, as well as the Euler parameterization
of the phase space are introduced. SU(2)-invariant classical systems are
discussed, and it is observed that the path of particle can be obtained by the
solution of a first-order equation, as the case with such models on commutative
spaces. The examples of free particle, rotationally-invariant potentials, and
specially the isotropic harmonic oscillator are investigated in more detail.Comment: 12+1 pages, no figs, LaTeX2
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