The regularization and determination of the Yang-Mills vacuum wave functional in three dimensions at O(e^2)

TL;DR

This paper advances the calculation of the three-dimensional Yang-Mills vacuum wave functional at weak coupling to O(e^2) accuracy using two regularized methods, providing detailed derivations and comparisons.

Contribution

It extends previous O(e) calculations to O(e^2) using two different regularized approaches, enhancing understanding of the Yang-Mills vacuum structure in three dimensions.

Findings

Successful computation of the vacuum wave functional at O(e^2)

Comparison of two different regularization methods

Detailed regularization procedure provided

Abstract

We complete the computation of the Yang-Mills vacuum wave functional in three dimensions at weak coupling with O(e^2) precision. We use two different methods to solve the functional Schroedinger equation. One of them generalizes to O(e^2) the method followed by Hatfield at O(e). The other uses the weak coupling version of the gauge invariant formulation of the Schroedinger equation and the ground state wave functional followed by Karabali, Nair, and Yelnikov. These methods need to be carefully regularized to yield correct results. This is done in this paper with full detail.