Variational Neural Network Approach to QFT in the Field Basis

Abstract

We present a variational neural network approach for solving quantum field theories in the field basis, focusing on the free Klein-Gordon model formulated in momentum space. While recent studies have explored neural-network-based variational methods for scalar field theory in position space, a systematic benchmark of the analytically solvable Klein-Gordon ground state -- particularly in the momentum-space field basis -- has been lacking. In this work, we represent the ground-state wavefunctional as a neural network defined on a discretized set of field configurations and train it by minimizing the Hamiltonian expectation value. This framework enables direct comparison to exact analytic results for a range of key observables, including the ground-state energy, two-point correlators, expectation value of the field, and the structure of the learned wavefunctional itself. Our results provide quantitative diagnostics of accuracy and demonstrate the suitability of momentum space for benchmarking neural network approaches, while establishing a foundation for future extensions to interacting models and position-space formulations.

References in corpus (15)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Deep neural network solution of the electronic Schrödinger equation
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• Continuous Matrix Product States for Quantum Fields
• Variational solution of the Yang-Mills Schrödinger equation in Coulomb gauge
• On the Yang-Mills wave functional in Coulomb gauge
• Calculus of continuous matrix product states
• Confinement and gluon propagator in Coulomb gauge QCD
• A variational approach to the QCD wave functional:Dynamical mass generation and confinement
• Testing Proposals for the Yang-Mills Vacuum Wavefunctional by Measurement of the Vacuum
• Diffusion Models as Stochastic Quantization in Lattice Field Theory
• Coulomb string tension, asymptotic string tension, and the gluon chain
• Variational Neural-Network Ansatz for Continuum Quantum Field Theory
• Approximating Relativistic Quantum Field Theories with Continuous Tensor Networks
• Variational Monte Carlo with Neural Network Quantum States for Yang-Mills Matrix Model