A Variational Approach to Quantum Field Theory

TL;DR

This paper explores using neural networks as variational ansatz in a non-perturbative approach to study strongly coupled quantum field theories, specifically scalar theories with quartic interactions.

Contribution

It introduces the use of neural networks as trial wave functions in the variational method for quantum field theories, advancing non-perturbative analysis techniques.

Findings

Neural networks can serve as effective variational ansatz in quantum field theory.

The approach provides upper bounds on energy eigenstates in scalar field models.

Potential for application to more complex theories like QCD.

Abstract

In strongly coupled field theories, perturbation theory cannot be employed to study the low-energy spectrum. Thus, non-perturbative techniques are required. We employ the variational method, a rigorous, non-perturbative approach which provides variational upper bounds on the energy eigenstates of the theory. An essential step in the variational method is the choice of trial wave function. In this work, we study the viability of employing a neural network as our variational ansatz. As a first step towards phenomenologically interesting strongly coupled theories like quantum chromodynamics, we study scalar field theories with quartic couplings.