The Continuity of the Gauge Fixing Condition $n\cdot \partial n\cdot A=0$ for $SU(2)$ Gauge Theory

Abstract

The continuity of the gauge fixing condition $n\cdot \partial n\cdot A=0$ for $SU(2)$ gauge theory on the manifold $R⨂S^1⨂S^1⨂S^1$ is studied here, where $n^{\mu }$ stands for directional vector along $x_i$-axis($i=1,2,3$). It is proved that the gauge fixing condition is continuous given that gauge potentials are differentiable with continuous derivatives on the manifold $R⨂S^1⨂S^1⨂S^1$ which is compact.

7 pages