Colorless operators in a non-associative quantum theory

TL;DR

This paper explores non-associative quantum operators, introducing the concept of colorless (white) operators analogous to gauge theory, and hypothesizes that only these white operators contribute to physical observables.

Contribution

It introduces the notion of white operators in non-associative quantum theory and hypothesizes their exclusive role in physical observables.

Findings

Associators/antiassociators for four non-associative operators are derived.

White operators are proposed to not contribute to associators/antiassociators.

Observables are conjectured to correspond only to white operators.

Abstract

The associators/antiassociators for the product of four non-associative operators are deduced. By analogy with SU(3) gauge theory the notion of colorless (white) operators is introduced. Some properties of white operators are considered. It is hypothesized that white operators do not give any contribution to corresponding associators/antiassociators. It is suggested that the observables in a non-associative quantum theory correspond to the white operators only.