Title: Geometric Quantum Field Theory for Condensed Matter

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

This paper presents a novel geometric quantum field theory (GQFT) framework for analyzing quantum field theories within condensed matter systems. We introduce a new approach that explicitly incorporates geometric constraints and topological properties, aiming to provide a deeper understanding of emergent phenomena observed in these systems. The core of this work involves extending standard field theory techniques to accommodate these geometric elements, thereby offering a fundamentally different perspective on the behavior of quantum fields within condensed matter. We detail the key mathematical components and demonstrate the framework's ability to successfully model a range of complex quantum phenomena, including the emergence of quantized vortices and topological phase transitions. The resulting theory provides a robust and mathematically sound tool for investigating the intricate interplay between quantum mechanics and geometric structures in condensed matter physics. This research will significantly advance the field by offering a more intuitive and powerful method for tackling problems previously intractable with traditional approaches.

DOI: 10.5281/zenodo.22195229

Related papers

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

Jincheng Zhang

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.

Sep 4, 20260 citations

Title: Geometric Phase Field Theory with Wavefunction Reconstruction

Jincheng Zhang

This paper presents a novel geometric phase field theory framework, centered around the concept of a 'Geometric Wavefunction Mapping' – a method for reconstructing the underlying wavefunction of complex systems directly from geometric properties. We explore how these properties, when properly mapped, can reveal fundamental quantum states and facilitate a deeper understanding of entanglement. The core mechanism involves a precise mapping process, aiming to establish a robust connection between geometric configurations and quantum states. This work proposes a shift from traditional wavefunction methods to a fundamentally geometric approach, potentially offering a more intuitive and powerful means of analyzing quantum systems. The investigation focuses on the potential for this technique to address challenges inherent in current wavefunction-based methods, particularly in handling highly complex systems and intractable quantum states. We outline the theoretical foundation, initial implementation, and preliminary results demonstrating the efficacy of the proposed method.

Aug 29, 20260 citations

Title: Quantum Geometry as a Foundation for Topological Information Theory

Jincheng Zhang

Quantum geometry, a novel approach to geometry rooted in quantum mechanics, offers a promising avenue for advancing topological information theory. This paper investigates the potential of quantum geometry as a fundamental building block, demonstrating how it can provide a framework for understanding quantum information's intricate interplay with topological properties. We introduce a dynamic geometric model leveraging quantum entanglement and topological fields to construct a system where the topological essence is inextricably linked to quantum information states. The core claim is that quantum geometry provides a deeper insight into the fundamental role of quantum information within topological structures, potentially uncovering previously unrecognized connections and offering a new perspective on the robustness and encoding of topological data. This work explores the conceptual and mathematical foundations of this framework, highlighting its potential to revolutionize our understanding of quantum information in the context of topological systems.

Sep 3, 20260 citations

Title: Dynamical Quantum Simulation of Complex Topological Defects

Jincheng Zhang

This research investigates a novel dynamical quantum simulation technique designed to accurately model the formation and dynamics of complex topological defects within materials. The core claim is to develop a quantum algorithm that captures the intricate interplay between quantum fluctuations and topological order, offering a fundamentally more accurate approach compared to existing simulation methods. This work will explore the application of quantum mechanics to simulate the evolution of topological defects, focusing on their interactions with quantum fluctuations. We outline a theoretical framework incorporating elements of quantum field theory and topological phase transitions to achieve this goal. The research will demonstrate the potential for this technique to provide valuable insights into the behavior of these critical defects, with implications for materials science and condensed matter physics.

Sep 6, 20260 citations

Title: Phase-Field Quantum Geometry (PFQ)

Jincheng Zhang

The field of quantum geometry is experiencing a resurgence, driven by the desire to understand and manipulate the fundamental structure of quantum systems. This paper introduces the Phase-Field Quantum Geometry (PFQ) framework, a novel approach to representing and manipulating geometric configurations within quantum systems. PFQ leverages the concept of phase fields to dynamically construct complex geometric structures, offering a powerful tool for studying quantum phenomena and potentially enabling new quantum technologies. The core mechanism focuses on an automated "Phase Field Mapping" algorithm, which constructs intricate geometric representations from quantum data. This paper presents a detailed explanation of the PFQ framework, including its mathematical foundations, algorithm implementation, and potential applications across diverse quantum systems. The research explores the advantages of PFQ compared to existing geometric techniques and highlights its potential to unlock deeper insights into quantum mechanics.

Sep 4, 20260 citations

Title: Quantum-Based Topological Geometry Algorithm

Jincheng Zhang

This paper presents a novel quantum simulation algorithm for topological geometry, designed to simulate complex geometric structures and topological relationships with enhanced accuracy. Traditional numerical methods often struggle to accurately capture intricate topological properties. We propose a framework leveraging quantum simulation to model these structures, enabling more precise results through computational techniques. This research focuses on the design of a quantum algorithm capable of exploring and understanding topological phenomena with significantly improved fidelity. The core mechanism involves employing quantum states to represent and manipulate geometric configurations, offering a pathway to overcome limitations of classical simulation techniques. The algorithm will demonstrate improvements in the resolution and accuracy of topological analysis, offering a powerful tool for research and development in the field of topology and geometric computation.

Sep 6, 20260 citations