AI 中文总结
该研究开发了一种泛函框架，将多种顶点分解统一为同一结构，可通过树展开扩展顶点分解至四点以上，适用于凝聚态与粒子物理等领域的量子场论。
AI 中文摘要
单粒子不可约顶点编码量子场论中的重正化相互作用，但由于其高维度以及对动量、频率等外部变量的非平凡依赖，其实际处理仍具挑战性。我们开发了一种泛函框架，该框架将顶点函数的图论内容代数重组为更高效的构建块，并揭示了若干已确立的顶点分解（如拼图、单玻色子交换、渐近类和对称估计量）是同一泛函结构的不同实现。基于复合场有效作用量的勒让德变换，该形式体系表明不同的顶点表示源于对复合自由度的不同选择。我们证明，在该框架中可通过树展开系统地获得高阶顶点，从而将上述分解扩展到四点水平之外。由于我们的发现不依赖于任何特定物理场景，该框架广泛适用于凝聚态物理、粒子物理等领域的量子场论。
英文摘要
One-particle irreducible vertices encode renormalized interactions in quantum field theories, but their practical treatment remains challenging due to their high dimensionality and nontrivial dependence on external variables such as momenta or frequencies. We develop a functional framework that algebraically reorganizes the diagrammatic content of the vertex functions into more efficient building blocks and reveals several established vertex decompositions, such as parquet, single-boson exchange, asymptotic classes and symmetric estimators, as different realizations of a common functional structure. Based on Legendre transforms of the effective action of composite fields, the formalism shows that different vertex representations arise from different choices of composite degrees of freedom. We demonstrate that in our framework higher-order vertices can be systematically obtained via tree expansions, thereby extending the aforementioned decompositions beyond the four-point level. Because our findings are independent of any specific physical setting, the framework applies broadly to quantum field theories in condensed matter physics, particle physics, and beyond.
Comments28 pages, 11 figures, 1 table
