Speaker
Description
We present a variational method for solving quantum field theories in the continuum field basis using neural networks. As a benchmark, we consider the free Klein–Gordon model in one spatial dimension, where the ground-state wavefunctional is known analytically. The variational ansatz is implemented using a feed-forward neural network trained to minimize the Hamiltonian expectation value in the Schr¨odinger picture. Our formulation preserves continuum-inspired operator structure by treating the canonical momentum as a functional derivative and discretizes only the momentum domain via Riemann summation. While our numerical results are computed at finite resolution with a momentum cutoff, the approach maintains close contact with the infinite-dimensional Hilbert space
of continuum QFT. We demonstrate accurate reproduction of ground-state observables—including energy, momentum-space two-point correlators, and field expectation values—and provide direct visualizations of the learned wavefunctional. This work establishes a flexible and physically interpretable framework for nonperturbative QFT, paving the way for future applications to interacting theories and gauge fields.
