Mathematical Background of Formalism of Operator Manifold

TL;DR

This paper explores the mathematical structure of operator manifolds, presenting a new approach to quantizing geometry that extends secondary quantization and combines quantum field and geometric aspects.

Contribution

It introduces a novel quantization scheme for geometry based on operator manifolds, expanding the method of secondary quantization with geometric objects.

Findings

Operator manifold provides a unified quantum and geometric framework.

New quantization of geometry differs fundamentally from previous schemes.

The approach broadens the mathematical understanding of quantum geometry.

Abstract

The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The nature of operator manifold provides its elements with both quantum field and geometry aspects, a detailed study of which is a subject of present paper. It yields a quantization of geometry differing in principle from all earlier suggested schemes.