Gauge fields, quantum interference, and holonomy transformations

The question of which quantities are measured when a gauge field is experimentally detected is investigated. The Josephson effect is considered in connection with this question and a generalization of this effect for non-Abelian gauge theories is obtained. It is shown that the gauge field in an n-dimensional manifold can be reconstructed from the holonomy transformations (parallel-transport operators around loops) for an n-dimensional set of loops. An application is given to Minkowski space-time compactified by the addition of null infinity. An equivalence principle for gauge fields is also formulated.