An algebraic method for solving the SU(3) Gauss law
Antti Salmela
TL;DR
This paper introduces an algebraic approach to solving the SU(3) Gauss law, extending previous SU(2) results by employing a non-Abelian Poincare lemma and analyzing singularities.
Contribution
It generalizes SU(2) solutions to SU(3) Gauss law using algebraic methods and explores the structure of the colour-electric and magnetic fields.
Findings
Solution to source-free SU(3) Gauss law using non-Abelian Poincare lemma
Decomposition of the colour-electric field with sources
Analysis of singularities from eigenvalue degeneracies
Abstract
A generalisation of existing SU(2) results is obtained. In particular, the source-free Gauss law for SU(3)-valued gauge fields is solved using a non-Abelian analogue of the Poincare lemma. When sources are present, the colour-electric field is divided into two parts in a way similar to the Hodge decomposition. Singularities due to coinciding eigenvalues of the colour-magnetic field are also analysed.
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