A non-associative quantum mechanics
High Energy Physics - Theory
2009-11-11 v5 High Energy Physics - Phenomenology
Rings and Algebras
Quantum Physics
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.
Cite
@article{arxiv.hep-th/0502216,
title = {A non-associative quantum mechanics},
author = {Vladimir Dzhunushaliev},
journal= {arXiv preprint arXiv:hep-th/0502216},
year = {2009}
}
Comments
one typo in Eq. (23) is corrected