The Deformation Philosophy, Quantization and Noncommutative Space-Time Structures

  • Daniel SternheimerEmail author
Part of the Progress in Mathematics book series (PM, volume 287)


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.

Deformation theory Deformation philosophy Quantization Quantum groups Antide Sitter Composite elementary particles Quantized space-time Cosmology,Baryogenesis 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsKeio UniversityYokohamaJapan

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