A non-associative quantum mechanics

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.

one typo in Eq. (23) is corrected

References in corpus (1)

• Three-cocycles, Nonassociative Gauge Transformations and Dirac's Monopole

Cited by in corpus (6)

• Quantum correlations are weaved by the spinors of the Euclidean primitives
• Extended GUP formulation and the role of momentum cut-off
• Geometrical Applications of Split Octonions
• Rotations in the Space of Split Octonions
• Algebraical Entropy and Arrow of Time
• Dirac and Maxwell systems in split octonions