Deep reinforcement learning for complex evaluation of one-loop diagrams in quantum field theory

Area of Science:

• Quantum Field Theory
• Computational Physics
• Machine Learning

Background:

• Analytic continuation is crucial for extracting physical quantities from correlators in quantum field theory.
• One-loop diagrams necessitate contour deformation in the complex plane to handle nonanalyticities.
• Existing numerical methods can be computationally intensive.

Purpose of the Study:

• To present a novel deep reinforcement learning (DRL) technique for numerical analytic continuation.
• To automate the complex contour deformations required in quantum field theory calculations.
• To demonstrate the feasibility of DRL for solving challenging integral equations.

Main Methods:

• A DRL agent was trained to perform contour deformations on loop integrals.
• The agent learned to navigate nonanalyticities in the complex momentum plane.
• A toy model with a known exact solution was used for training and validation.

Main Results:

• The DRL agent successfully performed numerical analytic continuation in the toy model.
• The technique demonstrated the ability to handle complex integration paths.
• The approach shows potential for application to nonperturbative calculations.

Conclusions:

• Deep reinforcement learning offers a promising new avenue for numerical analytic continuation.
• This method could enhance the computation of two-point functions and related problems.
• The DRL agent shows potential for deployment in iterative numerical schemes for complex domain problems.