Abstract
We find that the self-intersection of a closed curve (loop) is characterized by a jump in the self-linkage number of the loop. This is used to study the self-intersections of a mathematical closed curve evolving according to the Nambu action. We also show that segments of cosmic string cannot simply pass through one another at a self-intersection. Instead, intercommuting is found to be energetically favorable in the case of untwisted global strings.

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