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The Deformation Philosophy, Quantization and Noncommutative Space-Time Structures

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Higher Structures in Geometry and Physics

Part of the book series: Progress in Mathematics ((PM,volume 287))

Abstract

The role of deformations in physics and mathematics, especially the theory of deformations of algebras developed by Gerstenhaber in the 1960s, led to the deformation philosophy promoted in mathematical physics by Flato since the 1970s, exemplified by deformation quantization and its manifold avatars, including quantum groups and the “dual” aspect of quantum spaces. Deforming Minkowski space-time and its symmetry to anti de Sitter has significant physical consequences that we sketch (e.g., singleton physics). We end by presenting an ongoing program in which anti de Sitter would be quantized in some regions, speculating that this could explain baryogenesis in a universe in constant expansion and that higher mathematical structures could provide a unifying framework.

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Notes

  1. 1.

    I owe the quotation (in German) to the late Julius Wess.

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  1. Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan

    Daniel Sternheimer

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  1. Universität Zürich, Institut für Mathematik, Winterthurerstr. 190, Zürich, CH-8057, Switzerland

    Alberto S. Cattaneo

  2. Loyola University, Chicago, Department of Mathematics, Chicago, 60626, Illinois, USA

    Anthony Giaquinto

  3. Pennsylvania State University, Department of Mathematics, Eberly College of Science, University Park, 16802, Pennsylvania, USA

    Ping Xu

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Sternheimer, D. (2011). The Deformation Philosophy, Quantization and Noncommutative Space-Time Structures. In: Cattaneo, A., Giaquinto, A., Xu, P. (eds) Higher Structures in Geometry and Physics. Progress in Mathematics, vol 287. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4735-3_3

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