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Neural Wavefunctions in Quantum Field Theory I: Asymptotic Freedom
Paulo F. Bedaque, Hersh Kumar, Suryansh Rajawat, Gregory Ridgway·June 18, 2026
hep-lathep-phhep-thnucl-thQuantum Physics
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Abstract
We present a variational approach to quantum field theory based on wavefunctions parameterized by neural networks. While variational methods have a celebrated history across many fields, their application to quantum field theory has been limited by well-known challenges. We show that neural-network wavefunctions, combined with modern machine-learning techniques, enable competitive variational calculations in nontrivial field theories. As a demonstration, we reproduce the essential features of the two-dimensional nonlinear $σ$-model: asymptotic freedom, dynamical mass generation and the model's step-scaling function.