### 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) |
---|---|

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 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications In Mathematical Physics*,

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

}

*Communications In Mathematical Physics*, vol. 61, no. 1, pp. 69-85. https://doi.org/10.1007/BF01609468

**Moufang plane and octonionic Quantum Mechanics.** / Gunaydin, Murat; Piron, C.; Ruegg, H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Moufang plane and octonionic Quantum Mechanics

AU - Gunaydin, Murat

AU - Piron, C.

AU - Ruegg, H.

PY - 1978/2/1

Y1 - 1978/2/1

N2 - It is shown that the usual axioms of one-particle Quantum Mechanics can be implemented with projection operators belonging to the exceptional Jordan algebra J83 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 F4 is studied, as well as a possible relation with the color group SU(3) and quark confinement.

AB - It is shown that the usual axioms of one-particle Quantum Mechanics can be implemented with projection operators belonging to the exceptional Jordan algebra J83 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 F4 is studied, as well as a possible relation with the color group SU(3) and quark confinement.

UR - http://www.scopus.com/inward/record.url?scp=0001836402&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001836402&partnerID=8YFLogxK

U2 - 10.1007/BF01609468

DO - 10.1007/BF01609468

M3 - Article

AN - SCOPUS:0001836402

VL - 61

SP - 69

EP - 85

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -