The Operator Manifold Formalism. I

TL;DR

The paper introduces an operator manifold formalism that unifies geometry and field theory, incorporating multiworld geometry and internal worlds to address fundamental particle physics problems.

Contribution

It presents a novel operator manifold formalism and operator multimanifold framework, integrating spacetime and internal worlds with confinement and gauge principles.

Findings

Development of a unified geometric and field theoretical framework.

Introduction of multiworld geometry involving spacetime and internal worlds.

Application to key problems in particle physics.

Abstract

The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the spacetime continuum and internal worlds, where the subquarks are defined implying the Confinement and Gauge principles. This formalism in Part II (hep-th/9812182) is used to develop further the microscopic approach to some key problems of particle physics.