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化繁为简的局域化方法

Localization methods:simplifying complexity

  • 摘要: 量子场论的微扰论方法在解释物理学中的许多重要现象时面临失效的困境,而目前尚没有分析非微扰效应的一般理论框架。超对称的引入为突破这一瓶颈提供了关键路径。局域化方法充分利用超对称的特性,将无穷维泛函积分约化为方便处理的有限维积分、离散求和或矩阵积分,成为非微扰计算的核心工具。文章简要介绍局域化方法的基本思想,梳理该方法的发展脉络,揭示其在物理与数学交叉领域的深远影响。

     

    Abstract: Perturbative methods in quantum field theory often encounter limitations in explaining many crucial physical phenomena. Moreover, there remains a lack of general theoretical frameworks for analyzing non-perturbative effects. The introduction of supersymmetry provides a critical pathway to overcome this bottleneck. Leveraging the unique properties of supersymmetry, localization methods reduce infinite-dimensional functional integrals to manageable finite-dimensional integrals, discrete summations, or matrix integrals. This development has established localization methods as a cornerstone tool for non-perturbative computations. This article provides a concise overview of the fundamental principles of localization methods, traces their historical evolution, and highlights their profound implications at the intersection of physics and mathematics.

     

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