For html web material about this chart, click HERE. For a pdf file about this chart, click Here or go to physics/0102042 at arXiv.org.
Clifford Algebras (Discrete and Real) Octonions Jordan Algebras Lie Algebras von Neumann hyperfinite II1 factor
Segal Conformal Theory Internal Symmetry Space MacDowell-Mansouri Gravity Standard Model Weyl Groups Fermions HyperDiamond Feynman Checkerboard
Clifford algebra factorization Cl(8n) = Cl(n) x ...(tensor n times)... x Cl(n) gives generalized von Neumann hyperfinite II1 factor. The Discrete HyperDiamond Generalized Feynman Checkerboard and Continuous Manifolds are related by Quantum Superposition: Elements of a Discrete Clifford algebra correspond to Basis Elements of a Real Clifford algebra. General Elements of a Real Clifford algebra correspond to Superpositions of ( Basis Elements = Elements of the underlying Discrete Clifford algebra ). Volumes of Spaces of Superpositions of some given Sets of Basis Elements correspond to Mass or Charge of Particles or Forces represented by those Basis Elements. Volumes of Spaces of Superpositions of other given Sets of Basis Elements correspond to Volume of Physical SpaceTime and Volume of Internal Symmetry Space represented by those Basis Elements.
Tony Smith's Home Page