Trying to understand confinement in the Schroedinger picture

TL;DR

This paper explores the gauge-invariant Gaussian ansatz in the Schrödinger picture to understand confinement in Yang-Mills theory, highlighting its potential to reproduce key features like asymptotic freedom and linear quark potential.

Contribution

It demonstrates that the Schrödinger picture with a gauge-invariant Gaussian ansatz can systematically study confinement and related phenomena in Yang-Mills theory, offering advantages over Euclidean methods.

Findings

Potential to reproduce asymptotic freedom

Mass generation through dimensional transmutation

Linear potential between static quarks

Abstract

We study the gauge-invariant gaussian ansatz for the vacuum wave functional and show that it potentially possesses many desirable features of the Yang--Mills theory, like asymptotic freedom, mass generation through the transmutation of dimensions and a linear potential between static quarks. We point out that these (and other) features can be studied in a systematic way by combining perturbative and 1/n expansions. Contrary to the euclidean approach, confinement can be easily formulated and easily built in, if not derived, in the variational Schroedinger approach.