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

TL;DR

This paper develops a local quantum field theory framework in two dimensions by quantizing the Helmholtz equation with interactions, using the general boundary formulation to describe dynamics in finite regions and showing their equivalence to traditional methods.

Contribution

It introduces a local description of 2D quantum field theory using the general boundary formulation, emphasizing finite regions and demonstrating their equivalence to standard approaches.

Findings

Local quantum field theory description in 2D

Equivalence of boundary and traditional formulations

Application to finite disk and annulus regions

Abstract

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.