Toy models of a non-associative quantum mechanics

Toy models of a non-associative quantum mechanics are presented. The Heisenberg equation of motion is modified using a non-associative commutator. Possible physical applications of a non-associative quantum mechanics are considered. The idea is discussed that a non-associative algebra could be the operator language for the non-perturbative quantum theory. In such approach the non-perturbative quantum theory has observables and unobservables quantities.