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.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics