Feynman Diagrams as Computational Graphs

We propose a computational graph representation of high-order Feynman diagrams in Quantum Field Theory (QFT), applicable to any combination of spatial, temporal, momentum, and frequency domains. Utilizing the Dyson-Schwinger and parquet equations, our approach effectively organizes these diagrams in...

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Bibliographic Details
Published in:arXiv.org 2024-02
Main Authors: Hou, Pengcheng, Wang, Tao, Cerkoney, Daniel, Cai, Xiansheng, Li, Zhiyi, Deng, Youjin, Wang, Lei, Chen, Kun
Format: Article
Language:English
Subjects:
Electron gas
Elementary excitations
Feynman diagrams
Graph representations
Graphical representations
Machine learning
Mathematical analysis
Quantum field theory
Quantum theory
Redundancy
Tensors
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Summary:We propose a computational graph representation of high-order Feynman diagrams in Quantum Field Theory (QFT), applicable to any combination of spatial, temporal, momentum, and frequency domains. Utilizing the Dyson-Schwinger and parquet equations, our approach effectively organizes these diagrams into a fractal structure of tensor operations, significantly reducing computational redundancy. This approach not only streamlines the evaluation of complex diagrams but also facilitates an efficient implementation of the field-theoretic renormalization scheme, crucial for enhancing perturbative QFT calculations. Key to this advancement is the integration of Taylor-mode automatic differentiation, a key technique employed in machine learning packages to compute higher-order derivatives efficiently on computational graphs. To operationalize these concepts, we develop a Feynman diagram compiler that optimizes diagrams for various computational platforms, utilizing machine learning frameworks. Demonstrating this methodology's effectiveness, we apply it to the three-dimensional uniform electron gas problem, achieving unprecedented accuracy in calculating the quasiparticle effective mass at metal density. Our work demonstrates the synergy between QFT and machine learning, establishing a new avenue for applying AI techniques to complex quantum many-body problems.
ISSN:2331-8422