From Clifford Algebra of Nonrelativistic Phase Space to Quarks and Leptons of the Standard Model

Piotr Zenczykowski, Institute of Nuclear Physics, Krakow, Poland

The talk will review a Clifford-algebra-related approach to elementary particles recently presented in my book “Elementary Particles and Emergent Phase Space” (World Scientific). The proposed scheme succesfully explains several features of a single generation of elementary particles (as defined in the Standard Model). The review will contain several interrelated parts:

  1. BACKGROUND:
    • a philosophical background motivating a maximally symmetric treatment of position and momentum variables (whence phase space),
    • an analysis of what current theory and phenomenology really tell us about the concept of quark mass (i.e. the minimal assumptions needed in quark mass extraction procedures),
  2. CLIFFORD ALGEBRA of NONRELATIVISTIC PHASE SPACE
    • an introduction of a novel variation on Born's reciprocity idea which provides a new possible view on the problem of mass,
    • a presentation of author's original approach to space quantization based on Dirac-like linearization of nonrelativistic quadratic form $p^2+x^2$ (with momentum and position satisfying standard commutation relations), which leads to the emergence of internal quantum numbers naturally identifiable with isospin and colour,
  3. CONNECTION TO CURRENT MODELS OF ELEMENTARY PARTICLES
    • a comparison of the resulting Clifford-algebra-based explanation of a single generation of elementary particles with that provided by the celebrated Harari-Shupe rishon (subquark) model,
    • a discussion of how the additivity of momenta may be generalized and used in the construction of hadrons as composite systems of quarks, together with a proposal for a restoration of special relativity at the colourless hadronic level.