The quantum electromagnetic field in multiply connected space

A gauge-invariant and microscopically causal theory of the sourceless electromagnetic field in a topologically arbitrary globally hyperbolic asymptotically flat background metric is proposed. The topology manifests itself in an algebra of superselected quantities, one of which is the net (apparent) charge. Relative to a particular Cauchy hypersurface, the field resolves into a 'Coulombic' part generating the above algebra and a 'radiative' part expressible in terms of photon creation and destruction operators. An appendix extends 'Hodge theory' to non-compact, but asymptotically-flat three-manifolds. (author)