On the Loop Space Formulation of Gauge Theories

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We discuss a possible group theoretical approach to the loop description of gauge theories. In this approach classical configurations are interpreted as unitary representations of the "group of loops". The structure of this group is examined, and it is in particular shown how a metric can be introduced. Problems related to the local structure of the group are discussed, and it is suggested that a regularization of the theory should be connected to a possible generalization of Fourier transformations on groups. In this picture the description of the Yang-Mills field in terms of the Wilson loop average is dual to that of the Lagrangian formulation. We illustrate the ideas by some simple examples.