U(1) connection
= U(1) connection
{c}
{title2=$A,\quad F=dA$}
A connection on a principal circle bundle has local real <one-form> representatives $A$ transforming by $A\mapsto A+d\chi$. Its curvature is the globally defined <two-form> $F=dA$. In unit-charge normalization its <holonomy> around a closed loop is $e^{i\oint A}$, and curvature periods are integer multiples of $2\pi$ on closed surfaces. A circulation representative is defined modulo $2\pi$ under large <gauge transformations>.