Editing Dirac string (section)

==Details==
The quantization forced by the Dirac string can be understood in terms of the [[cohomology]] of the [[fibre bundle]] representing the gauge fields over the base manifold of space-time. The magnetic charges of a gauge field theory can be understood to be the group generators of the cohomology group <math>H^2(M)</math> for the fiber bundle ''M''.  The cohomology arises from the idea of classifying all possible gauge [[field strength]]s <math>F=dA</math>, which are manifestly [[exact form]]s, modulo all possible gauge transformations, given that the field strength ''F'' must be a [[closed and exact differential forms|closed form]]: <math>dF=0</math>.  Here, ''A'' is the [[vector potential]] and ''d'' represents the gauge-[[covariant derivative]], and ''F'' the field strength or [[curvature form]] on the fiber bundle. Informally, one might say that the Dirac string carries away the "excess curvature" that would otherwise prevent ''F'' from being a closed form, as one has that <math>dF=0</math> everywhere except at the location of the monopole.