A reparametrization invariant surface ordering

Journal article, 2005

We introduce a notion of a non-abelian loop gauge field defined on points in loop space. For this purpose we first find an infinite-dimensional tensor product representation of the Lie algebra which is particularly suited for fields on loop space. We define the non-abelian Wilson surface as a 'time' ordered exponential in terms of this loop gauge field and show that it is reparametrization invariant.