A generalization of the flat-space d'Adhemar formulation of Maxwell theory to asymptotically simple space-times is presented. The essential new ideas in this approach are the introduction of a nonlocal variable (the holonomy operator) for Maxwell theory used in conjunction with a nonlocal, conformally invariant, description of the background geometry of space-time. The field equations for this new variable are derived and an explicit relationship (in a perturbative sense) between the free data at $\mathcal{J}$ and the field at an interior point is given. The possible applications of this method to scattering theory and to the Einstein equations are discussed.

• Received 16 January 1990

DOI:https://doi.org/10.1103/PhysRevD.42.503