On Hypercomplex Extensions of Quantum Theory

TL;DR

This paper explores hypercomplex extensions of quantum theory, focusing on non-abelian phase wave descriptions, specialized Fock spaces, and Feynman methods for particle interactions with external fields.

Contribution

It introduces hypercomplex frameworks for quantum mechanics, extending traditional models to incorporate non-abelian phases and new interaction descriptions.

Findings

Development of quantum schemas for non-abelian phases

Construction of Fock spaces for hypercomplex structures

Application of Feynman recipe to hypercomplex quantum interactions

Abstract

This paper discusses quantum mechanical schemas for describing waves with non-abelian phases, Fock spaces of annihilation-creation operators for these structures, and the Feynman recipe for obtaining descriptions of particle interactions with external fields.