ICCA10

Tartu, 4–9 August 2014

10^{th} International Conference on Clifford Algebras and their Applications in Mathematical Physics

**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:

- 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),

- 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,

- 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.