Title: Quantum Geometry – Formalizing the Geometry of Quantum Systems Using Topological Concepts

Jincheng Zhang

Published Sep 4, 2026• 0 citations

Abstract

Quantum geometry, a nascent field, seeks to formalize the geometric properties of quantum systems through the lens of topology. This paper explores the development of a novel mathematical framework for defining and analyzing these geometric properties, explicitly incorporating topological concepts to enhance understanding and provide a more robust and insightful approach compared to traditional geometric methods. We propose a new methodology predicated on the observation that certain geometric features exhibit topological behavior, offering a fundamentally different perspective on the structure of quantum systems. The paper outlines the core mechanism, detailing how topological aspects will be integrated into the definition of geometric properties and how this will lead to a deeper comprehension of quantum phenomena. The investigation will focus on establishing a rigorous mathematical foundation for this approach, demonstrating its potential for improving the analysis of complex quantum systems.

DOI: 10.5281/zenodo.22290404

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