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A non-associative quantum mechanics. (English) Zbl 1099.81004
Summary: A nonassociative quantum mechanics is proposed in which the product of three and more operators can be nonassociative. The multiplication rules of the octonions define the multiplication rules of the corresponding operators with quantum corrections. The self-consistency of the operator algebra is proved for the product of three operators. Some properties of the nonassociative quantum mechanics are considered. It is proposed that some generalization of the nonassociative algebra of quantum operators can be helpful for understanding of the algebra of field operators with a strong interaction.

MSC:
81P05 General and philosophical questions in quantum theory
81R15 Operator algebra methods applied to problems in quantum theory
47N50 Applications of operator theory in the physical sciences
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References:
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