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

Understand

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.