Neural network expansion of Euclidean path integrals and its application to interacting scalar fields

Abstract

Studying phase transitions in interacting quantum field theories generally requires the numerical study of the dynamical system on a large lattice, which is, in most cases, computationally very challenging. In this work an alternative method is proposed to solve Euclidean path integrals in quantum field theories, using radial basis function-type neural networks. The method allows us to approximate observables in a very efficient manner, taking only seconds to do calculations that would otherwise take hours or even days with other existing methods. The model is used to describe phase transitions in the scalar $\ddot{I}{•}^4$ theory for a wide range of coupling strength. The obtained phase transition line is compared to previous lattice results, giving very good agreement between them.