Editing Chern–Simons theory (section)

===Wilson loops===

The [[observable]]s of Chern–Simons theory are the ''n''-point [[correlation function]]s of gauge-invariant operators. The most often studied class of gauge invariant operators are [[Wilson loops]]. A Wilson loop is the holonomy around a loop in ''M'', traced in a given [[representation of a Lie group|representation]] ''R'' of ''G''. As we will be interested in products of Wilson loops, without loss of generality we may restrict our attention to [[representation theory#Subrepresentations, quotients, and irreducible representations|irreducible representation]]s ''R''.

More concretely, given an irreducible representation ''R'' and a loop ''K'' in ''M'', one may define the Wilson loop <math>W_R(K)</math> by

:<math> W_R(K) =\operatorname{Tr}_R \, \mathcal{P} \exp\left(i \oint_K A\right)</math>

where ''A'' is the connection 1-form and we take the [[Cauchy principal value]] of the [[contour integral]] and <math>\mathcal{P} \exp</math> is the [[path-ordered exponential]].