The Yang-Mills vacuum wave functional in three dimensions at weak coupling

TL;DR

This paper calculates the three-dimensional Yang-Mills vacuum wave functional at weak coupling using two methods, providing a detailed comparison and advancing understanding of non-Abelian gauge theories in this regime.

Contribution

It introduces two approaches to compute the vacuum wave functional at O(e^2) and compares their results, extending previous weak coupling analyses.

Findings

Both methods yield consistent results at O(e^2)

The comparison highlights differences in the approaches

Provides insights into the structure of the vacuum state

Abstract

We compute 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 Schroedinger functional 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. We compare both results and discuss the differences between them.