Hamilton's equations in a non-associative quantum theory

TL;DR

This paper proposes a novel non-associative algebra framework for quantum field quantization, introduces associator calculations, and suggests a generalized form of Hamilton's equations, potentially unifying quantum theories.

Contribution

It introduces a new non-associative algebra for quantization, provides associator calculation algorithms, and generalizes Hamilton's equations for non-associative quantum theories.

Findings

A new non-associative algebra for quantum fields.

Algorithms for associator calculations of operators.

Arguments for non-associative quantum theory as a unifying framework.

Abstract

A new non-associative algebra for the quantization of strongly interacting fields is proposed. The full set of quantum $(\pm)$associators for the product of three operators is offered. An algorithm for the calculation of some $(\pm)$associators for the product of some four operators is offered. The possible generalization of Hamilton's equations for a non-associative quantum theory is proposed. Some arguments are given that a non-associative quantum theory can be a fundamental unifying theory.