### Abstract

It is shown that the usual axioms of one-particle Quantum Mechanics can be implemented with projection operators belonging to the exceptional Jordan algebra J_{8}^{3} over real octonions. Certain lemmas on these projection operators are proved by elementary means. Use is made of the Moufang projective plane. It is shown that this plane can be orthocomplemented and that there exists a unique probability function. The result of successive, compatible experiments is shown not to depend on the order in which they are performed, in spite of the non-associativity of octonion multiplication. The algebra of observables and the action of the exceptional group F_{4} is studied, as well as a possible relation with the color group SU(3) and quark confinement.

Original language | English (US) |
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Pages (from-to) | 69-85 |

Number of pages | 17 |

Journal | Communications In Mathematical Physics |

Volume | 61 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1 1978 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Communications In Mathematical Physics*,

*61*(1), 69-85. https://doi.org/10.1007/BF01609468