  We present a gauge-theoretic interpretation of the "analytic" version of the
geometric Langlands program, in which Hitchin Hamiltonians and Hecke operators
are viewed as concrete operators acting on a Hilbert space of quantum states.
The gauge theory ingredients required to understand this construction -- such
as electric-magnetic duality between Wilson and 't Hooft line operators in
four-dimensional gauge theory -- are the same ones that enter in understanding
via gauge theory the more familiar formulation of geometric Langlands, but now
these ingredients are organized and applied in a novel fashion.
