Three features—transition probabilities, connectedness, and homogeneity—are proposed as bare necessities for quantum models, yielding atomic JBW factors and one known E6-symmetric space.
Exceptional Projective Geometries and Internal Symmetries
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abstract
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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quant-ph 1years
2026 1verdicts
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The bare necessities of a physically reasonable mathematical model for quantum theory
Three features—transition probabilities, connectedness, and homogeneity—are proposed as bare necessities for quantum models, yielding atomic JBW factors and one known E6-symmetric space.