Feynman Diagrams as Computational Graphs
<|reference_start|>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 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.<|reference_end|>
@article{hou2024feynman,
    title={Feynman Diagrams as Computational Graphs},
    author={Pengcheng Hou, Tao Wang, Daniel Cerkoney, Xiansheng Cai, Zhiyi Li,
  Youjin Deng, Lei Wang, and Kun Chen},
    journal={arXiv preprint arXiv:2403.18840},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.18840},
    primaryClass={hep-th cond-mat.str-el cs.LG hep-ph physics.comp-ph}
}