Feynman Diagrams as Computational Graphs

• URL: http://arxiv.org/abs/2403.18840v1
• Date: Wed, 28 Feb 2024 03:45:55 GMT
• Title: Feynman Diagrams as Computational Graphs
• Authors: Pengcheng Hou, Tao Wang, Daniel Cerkoney, Xiansheng Cai, Zhiyi Li, Youjin Deng, Lei Wang, Kun Chen,
• Abstract summary: We propose a computational graph representation of high-order Feynman diagrams in Quantum Field Theory (QFT) Our approach effectively organizes these diagrams into a fractal structure of tensor operations, significantly reducing computational redundancy. Our work demonstrates the synergy between QFT and machine learning, establishing a new avenue for applying AI techniques to complex quantum many-body problems.
• Score: 6.128507107025731
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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