Advances in Applied Clifford Algebras

, Volume 18, Issue 3–4, pp 543–556 | Cite as

A Spin Gauge Model of a Family of Particles

  • J. S. Roy Chisholm
  • Ruth S. Farwell


We have defined our spin gauge model of the electron and neutrino using the ‘physical algebra’ Cℓ(1, 6). We used our new form of ‘two-sided’ gauge transformations on spinors; these are equivalence transformations on minimal left ideals of the algebra. This equivalence transformation produces an additional interaction term which reproduces the correct electroweak interactions of the electron and neutrino, based on a reduced symmetry group. In the work presented here, this model is extended to the next physical algebra Cℓ(3, 8) which enables us to include the first family of particles. The strong interactions are generated by gauge transformation based on an SU(3) symmetry group which fixes the electric charges of the particles.


Clifford algebras gauge theories Lie algebras 

Mathematics Subject Classification (2000).

15A66 70S15 17B81 


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Copyright information

© Birkhauser 2008

Authors and Affiliations

  1. 1.Institute of Mathematics and StatisticsUniversity of KentCanterbury, KentUK
  2. 2.Buckinghamshire Chilterns University CollegeHigh Wycombe, BucksUK

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