Decomposition of the SU(2) gauge field in the Maximal Abelian gauge

TL;DR

This paper decomposes the SU(2) gauge field in the Maximal Abelian gauge into monopole and monopoleless parts, analyzing their contributions to the static potential and the confinement mechanism in lattice gauge theory.

Contribution

It introduces a method to separate monopole and monopoleless components of SU(2) gauge fields and analyzes their individual roles in confinement and string dynamics.

Findings

Monopole component produces a linear confining potential.

Modified nonabelian component yields a nonconfining potential.

Sum of potentials closely approximates the full nonabelian potential.

Abstract

We study decomposition of $SU(2)$ gauge field into monopole and monopoleless components. After fixing the Maximal Abelian gauge in $SU(2)$ lattice gauge theory we decompose the nonabelian gauge field into the Abelian field created by monopoles and the modified nonabelian field with monopoles removed. We then calculate respective static potentialis and show that the potential due to the modified nonabelian field is nonconfining while, as is well known, the Abelian field produces linear potential. We further find that the sum of these potentials approximates the nonabelian static potential with good precision at all distances considered. We conclude that at large distances the monopole field potential describes the classical energy of the hadronic string while the static potential due to the modified nonabelian field describes the string fluctuations energy.