A Mathematical Construction of the Non-Abelian Chern-Simons Functional Integral

We construct rigorously an infinite dimensional distribution which corresponds to the Chern-Simons (CS) functional integral associated with a principal fiber bundle over R ³ with structure group a compact connected Lie group. We determine the ‘moments’ of the CS distribution and show that these coincide with those used in informal studies of the CS integral. A locality property of the CS distribution is proven. The complexified theory of Fr?hlich and King is also discussed within our framework. Received: 2 April 1996 / Accepted: 15 August 1996