gauge theory associated to $\lambda $ assigns to each $G$-bundle with connection on the circle the complex number $\lambda (g)$, where $g$ is the holonomy. This is what physicists term the ‘exponentiated action’ of the theory. Notice that holonomy depends on an orientation on the circle, so this is a theory of *oriented* 0- and 1-manifolds. To the unique connection on a point is attached the trivial complex line ${{\mathbb C}}$; the automorphism group $G$ of the unique connection acts on ${{\mathbb C}}$ via $\lambda $. More precisely, this is correct if the point is positively oriented; for the negatively oriented point the action is via $\lambda {^{-1}}$. Now the standard quantization procedure constructs a theory $F$ with $F(\operatorname{pt}_+)$ the elements in ${{\mathbb C}}$ invariant under the action of the automorphisms. (This is called the ‘Gauss law’ in physics.) The result is the zero vector space if $\lambda \not= 1$ is nontrivial and is ${{\mathbb C}}$ if $\lambda =1$ is trivial. Then $F({\ensuremath{S^1}})=0$ in the first case and $F({\ensuremath{S^1}})=1$ in the second, as $F({\ensuremath{S^1}})=\dim F(\operatorname{pt}_+)$. These values may be understood as the result of the path integral over the groupoid $G{/\!/}G$ of connections on ${\ensuremath{S^1}}$ with respect to Haar measure: 