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    Wyświetlanie 1-6 z 6
    Tytuł:
    Matematyka i kosmologia
    Mathematics and Cosmology
    Autorzy:
    Heller, Michał
    Powiązania:
    https://bibliotekanauki.pl/articles/691306.pdf
    Data publikacji:
    2012
    Wydawca:
    Copernicus Center Press
    Tematy:
    mathematics
    cosmology
    noncommutative geometry
    Opis:
    The mathematical and cosmological works of a group associated with the Copernicus Center for Interdisciplinary Studies in Cracow are summarized. The group consists mainly of M. Heller, L. Pysiak, W. Sasin, Z. Odrzygóźdź and J. Gruszczak. The first paper by members of the group was published in 1988, and research has been continued to the present day. The main mathematical tool used in the first part of the group’s activity was the theory of differential spaces and, in the second, methods of noncommutative geometry. Among the main topics investigated have been classical singularities in relativistic cosmology and the unification of general relativity with quantum mechanics.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2012, 50; 63-74
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The existence of singularities and the origin of space-time
    Autorzy:
    Heller, Michał
    Powiązania:
    https://bibliotekanauki.pl/articles/690562.pdf
    Data publikacji:
    2008
    Wydawca:
    Copernicus Center Press
    Tematy:
    noncommutative geometry
    singularities
    space-time
    von Neumann algebras
    Opis:
    Methods of noncommutative geometry are applied to deal with singular space-times in general relativity. Such space-times are modeled by noncommutative von Neumann algebras of random operators. Even the strongest singularities turn out to be probabilistically irrelevant. Only when one goes to the usual (commutative) regime, via a suitable transition process, space-time emerges and singularities become significant.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2008, 43; 35-43
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Quantum geometry, logic and probability
    Autorzy:
    Majid, Shahn
    Powiązania:
    https://bibliotekanauki.pl/articles/1047619.pdf
    Data publikacji:
    2020-12-29
    Wydawca:
    Copernicus Center Press
    Tematy:
    logic
    noncommutative geometry
    digital geometry
    quantum gravity
    duality
    power set
    Heyting algebra
    Opis:
    Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. However, these ‘lattice spacing’ weights do not have to be independent of the direction of the arrow. We use this greater freedom to give a quantum geometric interpretation of discrete Markov processes with transition probabilities as arrow weights, namely taking the diffusion form ∂+f = (−Δθ + q − p)f for the graph Laplacian Δθ, potential functions q, p built from the probabilities, and finite difference ∂+ in the time direction. Motivated by this new point of view, we introduce a ‘discrete Schrödinger process’ as ∂+ψ = ı(−Δ + V )ψ for the Laplacian associated to a bimodule connection such that the discrete evolution is unitary. We solve this explicitly for the 2-state graph, finding a 1-parameter family of such connections and an induced ‘generalised Markov process’ for f = |ψ|2 in which there is an additional source current built from ψ. We also mention our recent work on the quantum geometry of logic in ‘digital’ form over the field F2 = {0, 1}, including de Morgan duality and its possible generalisations.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2020, 69; 191-236
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nieprzemienne rachunki prawdopodobieństwa
    Noncommutative calculi of probabilty
    Autorzy:
    Heller, Michał
    Powiązania:
    https://bibliotekanauki.pl/articles/690918.pdf
    Data publikacji:
    2010
    Wydawca:
    Copernicus Center Press
    Tematy:
    theory of probability
    noncommutative theory of probability
    algebra
    noncommutative geometry
    quantum mechanics
    probability measures
    Opis:
    The paper can be regarded as a short and informal introduction to noncommutative calculi of probability. The standard theory of probability is reformulated in the algebraic language. In this form it is readily generalized to that its version which is virtually present in quantum mechanics, and then generalized to the so-called free theory of probability. Noncommutative theory of probability is a pair (M, φ) where M is a von Neumann algebra, and φ a normal state on M which plays the role of a noncommutative probability measure. In the standard (commutative) theory of probability, there is, in principle, one mathematically interesting probability measure, namely the Lebesgue measure, whereas in the noncommutative theories there are many nonequivalent probability measures. Philosophical implications of this fact are briefly discussed.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2010, 47; 38-53
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some remarks on quantum and braided group gauge theory
    Autorzy:
    Majid, Shahn
    Powiązania:
    https://bibliotekanauki.pl/articles/1342806.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    bosonisation
    gauge theory
    connection
    braided group
    quantum group
    fiber bundle
    noncommutative geometry
    Opis:
    We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzeziński and the author) to braided group gauge theory and coalgebra gauge theory. We outline the diagrammatic version of the braided case. The bosonisation of any braided group provides us a trivial principal bundle in three ways.
    Źródło:
    Banach Center Publications; 1997, 40, 1; 335-349
    0137-6934
    Pojawia się w:
    Banach Center Publications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Geneza prawdopodobieństwa
    The origin of probability
    Autorzy:
    Heller, Michał
    Powiązania:
    https://bibliotekanauki.pl/articles/690886.pdf
    Data publikacji:
    2006
    Wydawca:
    Copernicus Center Press
    Tematy:
    probability theory
    dynamics
    noncommutative geometry
    free calculus of probability
    classical probability
    quantum probability
    Opis:
    After briefly reviewing classical and quantum aspects of probability, basic concepts of the noncommutative calculus of probability (called also free calculus of probability) and its possible application to model the fundamental level of physics are presented. It is shown that the pair (M, *), where M is a (noncommutative) von Neumann algebra, and a state on it, is both a dynamical object and a probabilistic object. In this way, dynamics and probability can be unified in noncommutative geometry. Some philosophical consequences of such an approach are indicated.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2006, 38; 61-75
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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