Dimensional Reduction
  Using an octonionic formalism, we introduce a new mechanism for reducing 10 spacetime dimensions to 4 without compactification. Applying this mechanism to the free, 10-dimensional, massless (momentum space) Dirac equation results in a particle spectrum consisting of exactly 3 generations. Each generation contains 1 massive spin-1/2 particle with 2 spin states, 1 massless spin-1/2 particle with only 1 helicity state, and their antiparticles --- precisely one generation of leptons. There is also a single massless spin-1/2 particle/antiparticle pair with the opposite helicity and no generation structure.   We conclude with a discussion of some further consequences of this approach, including those which could arise when using the formalism on a curved spacetime background, as well as the implications for the nature of spacetime itself. 
Corinne A. Manogue and Tevian Dray