  As a warmup for studying dynamics and gravitons in loop quantum gravity,
Varadajan showed that Wilson loops give operators on the Fock space for
electromagnetism in Minkowski spacetime - but only after regularizing the loops
by smearing them with a Gaussian. Unregularized Wilson loops are too singular
to give densely defined operators. Here we present a rigorous treatment of
unsmeared Wilson loops for vacuum electromagnetism on an arbitrary globally
hyperbolic static spacetime. Our Wilson loops are not operators, but
"quasioperators": sesquilinear forms on the dense subspace of Fock space
spanned by coherent states corresponding to smooth classical solutions. To
obtain this result we begin by carefully treating electromagnetism on globally
hyperbolic static spacetimes, addressing various issues that are usually
ignored, such as the definition of Aharonov-Bohm modes when space is
noncompact. We then use a new construction of Fock space based on coherent
states to define Wilson loop quasioperators. Our results also cover "Wilson
surfaces" in p-form electromagnetism.
