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We quantize the Helmholtz equation (plus perturbative interactions) in twodimensions to illustrate a manifestly local description of quantum fieldtheory. Using the general boundary formulation we describe the quantum dynamicsboth in a traditional time evolution setting as well as in a setting referringto finite disk (or annulus) shaped regions of spacetime. We demonstrate thatboth descriptions are equivalent when they should be.

States and amplitudes for finite regions in a two-dimensional Euclidean quantum field theory