45,329 research outputs found
Fuzzy Topology, Quantization and Gauge Invariance
Dodson-Zeeman fuzzy topology considered as the possible mathematical
framework of quantum geometric formalism. In such formalism the states of
massive particle m correspond to elements of fuzzy manifold called fuzzy
points. Due to their weak (partial) ordering, m space coordinate x acquires
principal uncertainty dx. It's shown that m evolution with minimal number of
additional assumptions obeys to schroedinger and dirac formalisms in
norelativistic and relativistic cases correspondingly. It's argued that
particle's interactions on such fuzzy manifold should be gauge invariant.Comment: 12 pages, Talk given on 'Geometry and Field Theory' conference,
Porto, July 2012. To be published in Int. J. Theor. Phys. (2015
The compositional rule of inference with several relations
The compositional rule of inference with several relations, which is the mainly used inference rule in approximate reasoning, is considered in this paper. Stability results are given and exact computational formulae are provided
Convergence of Fuzzy Tori and Quantum Tori for the quantum Gromov-Hausdorff Propinquity: an explicit approach
Quantum tori are limits of finite dimensional C*-algebras for the quantum
Gromov-Hausdorff propinquity, a metric defined by the author as a strengthening
of Rieffel's quantum Gromov-Hausdorff designed to retain the C*-algebraic
structure. In this paper, we propose a proof of the continuity of the family of
quantum and fuzzy tori which relies on explicit representations of the
C*-algebras rather than on more abstract arguments, in a manner which takes
full advantage of the notion of bridge defining the quantum propinquity.Comment: 41 Pages. This paper is the second half of ArXiv:1302.4058v2. The
latter paper has been divided in two halves for publications purposes, with
the first half now the current version of 1302.4058, which has been accepted
in Trans. Amer. Math. Soc. This second half is now a stand-alone paper, with
a brief summary of 1302.4058 and a new introductio
(Quantum) Space-Time as a Statistical Geometry of Fuzzy Lumps and the Connection with Random Metric Spaces
We develop a kind of pregeometry consisting of a web of overlapping fuzzy
lumps which interact with each other. The individual lumps are understood as
certain closely entangled subgraphs (cliques) in a dynamically evolving network
which, in a certain approximation, can be visualized as a time-dependent random
graph. This strand of ideas is merged with another one, deriving from ideas,
developed some time ago by Menger et al, that is, the concept of probabilistic-
or random metric spaces, representing a natural extension of the metrical
continuum into a more microscopic regime. It is our general goal to find a
better adapted geometric environment for the description of microphysics. In
this sense one may it also view as a dynamical randomisation of the causal-set
framework developed by e.g. Sorkin et al. In doing this we incorporate, as a
perhaps new aspect, various concepts from fuzzy set theory.Comment: 25 pages, Latex, no figures, some references added, some minor
changes added relating to previous wor
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