“The Important Thing is not to Stop Questioning”, Including the Symmetries on Which is Based the Standard Model

  • Daniel SternheimerEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)


New fundamental physical theories can, so far a posteriori, be seen as emerging from existing ones via some kind of deformation. That is the basis for Flato’s “deformation philosophy”, of which the main paradigms are the physics revolutions from the beginning of the twentieth century, quantum mechanics (via deformation quantization) and special relativity. On the basis of these facts we describe two main directions by which symmetries of hadrons (strongly interacting elementary particles) may “emerge” by deforming in some sense (including quantization) the Anti de Sitter symmetry (AdS), itself a deformation of the Poincaré group of special relativity. The ultimate goal is to base on fundamental principles the dynamics of strong interactions, which originated half a century ago from empirically guessed “internal” symmetries. After a rapid presentation of the physical (hadrons) and mathematical (deformation theory) contexts, we review a possible explanation of photons as composites of AdS singletons (in a way compatible with QED) and of leptons as similar composites (massified by 5 Higgs, extending the electroweak model to 3 generations). Then we present a “model generating” multifaceted framework in which AdS would be deformed and quantized (possibly at root of unity and/or in manner not yet mathematically developed with noncommutative “parameters”). That would give (using deformations) a space-time origin to the “internal” symmetries of elementary particles, on which their dynamics were based, and either question, or give a conceptually solid base to, the Standard Model, in line with Einstein’s quotation: “The important thing is not to stop questioning. Curiosity has its own reason for existing.”


Symmetries of hadrons models Anti de Sitter deformation theory deformation quantization singletons quantum groups at root of unity “quantum deformations” 


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Copyright information

© Daniel Sternheimer 2014

Authors and Affiliations

  1. 1.Department of MathematicsRikkyo UniversityTokyoJapan
  2. 2.Institut de Mathématiques de BourgogneUniversité de BourgogneDijon CedexFrance

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