Abstract
It is shown that the usual axioms of one-particle Quantum Mechanics can be implemented with projection operators belonging to the exceptional Jordan algebraJ 38 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 groupF 4 is studied, as well as a possible relation with the color group SU(3) and quark confinement.
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Communicated by R. Haag
Work supported by the Swiss National Science Foundation
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Günaydin, M., Piron, C. & Ruegg, H. Moufang plane and octonionic Quantum Mechanics. Commun.Math. Phys. 61, 69–85 (1978). https://doi.org/10.1007/BF01609468
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DOI: https://doi.org/10.1007/BF01609468