Exceptional Projective Geometries and Internal Symmetries

Details Exceptional Projective Geometries and Internal Symmetries Exceptional Projective Geometries and Internal Symmetries

2003-02-11

arxiv.org/abs/hep-th/0302079v1

Physics

High Energy Physics

High Energy Physics - Theory

37 pages, 6 figures

Scientific paper

A new mneumonic device is shown to emerge in connection with O(7) numerical tensors exhibiting duality and reflecting the natural 7=(4+3) splitting of 7-dimensional space. Then Desargues' and Pappus' theorems are shown to be connected through a geometry that makes use of octonionic numbers exhibiting this duality. Construction of exceptional Hilbert space based on Jordan algebras and exceptional projective geometries is illustrated. A brief discussion of the Moufang plane and non-Desarguesian geometries is presented.

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