  In this article, we express the Alexander polynomial of null-homologous long
knots in punctured rational homology $3$-spheres in terms of integrals over
configuration spaces. To get such an expression, we use a previously
established formula, which gives generalized Bott-Cattaneo-Rossi invariants in
terms of the Alexander polynomial and vice versa, and we relate these
Bott-Cattaneo-Rossi invariants to the perturbative expansion of Chern-Simons
theory.
