Pedagogical Reflections on Color Confinement in Chromostatics

TL;DR

This paper compares abelian and nonabelian gauge invariant states in chromostatics, highlighting differences in physical state representations and the gauge invariance of electrostatic states.

Contribution

It provides a pedagogical analysis of gauge invariance and physical states in chromostatics, emphasizing the role of Faraday lines and the limitations of gauge invariance in nonabelian theories.

Findings

Abelian electrostatic states can be viewed as point charges connected by Faraday lines.

Gauge invariance of electrostatic states holds only in the abelian case.

Yang-Mills equations lack direct physical content beyond their relation to physical states.

Abstract

Abelian and nonabelian gauge invariant states are directly compared to revisit how the unconfined abelian theory is expressed. It is argued that the Yang-Mills equations have no obvious physical content apart from their relation to underlying physical states. The main observation is that the physical states of electrostatics can be regarded as point charges connected by a uniform superposition of all possible Faraday lines. These states are gauge invariant only in the abelian case.