Moufang plane and octonionic Quantum Mechanics

M. Günaydin; C. Piron; H. Ruegg

doi:10.1007/BF01609468

Moufang plane and octonionic Quantum Mechanics

M. Günaydin, C. Piron, H. Ruegg

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75 Scopus citations

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 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.

Original language	English (US)
Pages (from-to)	69-85
Number of pages	17
Journal	Communications In Mathematical Physics
Volume	61
Issue number	1
DOIs	https://doi.org/10.1007/BF01609468
State	Published - Feb 1978

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01609468

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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.

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Moufang plane and octonionic Quantum Mechanics

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All Science Journal Classification (ASJC) codes

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