States and amplitudes for finite regions in a two-dimensional Euclidean   quantum field theory
  We quantize the Helmholtz equation (plus perturbative interactions) in two dimensions to illustrate a manifestly local description of quantum field theory. Using the general boundary formulation we describe the quantum dynamics both in a traditional time evolution setting as well as in a setting referring to finite disk (or annulus) shaped regions of spacetime. We demonstrate that both descriptions are equivalent when they should be. 
Daniele Colosi (UNAM), Robert Oeckl (UNAM)