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Isn't a Wilson loop the path ordered product taken over a closed path and which is then traced over (i.e. its character for some irreducible rep) (resulting in a complex number) while a Wilson line the corresponding untraced (so it still takes on values in the gauge Lie group) product over a path which needn't be closed in general? Wilson lines can be contracted with charged fields at both of its endpoints to give a complex number. Phys 19:28, 24 Jul 2004 (UTC)