A non-associative quantum mechanics

TL;DR

This paper introduces a non-associative quantum mechanics framework based on octonion algebra, exploring its properties and potential applications to strongly interacting quantum fields.

Contribution

It proposes a novel non-associative operator algebra using octonions and demonstrates its self-consistency, offering a new approach to quantum mechanics.

Findings

Operator algebra based on octonions is self-consistent.

Non-associative quantum mechanics can model strongly interacting fields.

Potential for new insights into quantum field operator structures.

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.