The study of the configurational statistical mechanics of polymers in
elongational flows requires the evaluation of quadratic path integrals
. Here we present a new technique for the evaluation of such path inte
grals; the method relies on Ito excursion theory and the Ray-Knight th
eorem from probability theory. In addition to providing a powerful com
putational method in standard cases, the method generalizes to deal wi
th quadratic path integrals for branching processes.