Monte Carlo evaluation of the continuum limit of the two-point function of the Euclidean free real scalar field subject to affine quantization

TL;DR

This paper uses Monte Carlo simulations to analyze the two-point function of a free scalar field in the continuum limit, comparing canonical and affine quantization methods on four-dimensional lattices.

Contribution

It demonstrates that affine quantization provides meaningful numerical results for the two-point function where exact solutions are unavailable.

Findings

Affine quantization yields viable two-point function results near the continuum limit.

Monte Carlo methods effectively evaluate quantum field theories on lattices.

Comparison between canonical and affine quantization highlights their differences in numerical outcomes.

Abstract

We study canonical and affine versions of the quantized covariant Euclidean free real scalar field-theory on four dimensional lattices through the Monte Carlo method. We calculate the two-point function at small values of the bare coupling constant and near the continuum limit at finite volume. Our investigation shows that affine quantization is able to give meaningful results for the two-point function for which is not available an exact analytic result and therefore numerical methods are necessary.