A mathematical construction of the non-Abelian Chern-Simons functional integral
Let CS be the Chern-Simons action functional on the space \({\mathcal A}\) of connections on a bundle over \(\mathbb{R}^3\). In this paper is given a realisation of normalised integrals of the form \(\int_{\mathcal A} e^{i\text{CS} (A)} \varphi(A) DA\) as \(\Phi_{\text{CS}} (\varphi)\), where \(\Phi_{\text{CS}}\) is an element of a Sobolev-type closure of a space \(L^2 (\mu)\). Properties of \(\Phi_{\text{CS}}\) are studied; in particular the moments are determined. Indications as to how these apply to knot theory are also given.
scientific article; zbMATH DE number 1057289