  We present a rigorous quantization scheme that yields a quantum field theory
in general boundary form starting from a linear field theory. Following a
geometric quantization approach in the K\"ahler case, state spaces arise as
spaces of holomorphic functions on linear spaces of classical solutions in
neighborhoods of hypersurfaces. Amplitudes arise as integrals of such functions
over spaces of classical solutions in regions of spacetime. We prove the
validity of the TQFT-type axioms of the general boundary formulation under
reasonable assumptions. We also develop the notions of vacuum and coherent
states in this framework. As a first application we quantize evanescent waves
in Klein-Gordon theory.
