Constrained path integrals and cosmic string self-intersections

We present a path integral formulation of the cosmic string self-intersection problem which exploits the fact that strings can be regarded as continuous approximations to discrete random walks. The problem is initially set up for free strings in flat space-time where techniques using the Kibble-Turok sphere are employed. In this picture, the relevant constraint is given by the Gaussian linkage of two closed curves. We then treat the intersection problem for closed loops subject to conservative forces. In both cases, the probability for a loop to intersect itself is computed in terms of the eigenvalues of a certain differential operator. (orig.)