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A non-associative quantum mechanics

Vladimir Dzhunushaliev
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Abstract

A non-associative quantum mechanics is proposed in which the product of three and more operators can be non-associative one. 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 non-associative quantum mechanics are considered. It is proposed that some generalization of the non-associative algebra of quantum operators can be helpful for understanding of the algebra of field operators with a strong interaction.

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Vladimir Dzhunushaliev. 2005-12-16. A non-associative quantum mechanics. https://doi.org/10.1007/s10702-006-0373-2

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