Algebraic and Functor Quantum Field Theory

In 2009, Urs Schreiber published “Algebraic Quantum Field Theory from n-functorial Quantum Field Theory,” relating the Haag-Kastler axiomatization of Quantum Field Theory (corresponding to the Heisenberg perspective) on 2-dimensional Minkowski spacetime to that of Atiyah and Segal (Schrödinger). In this paper, we seek to provide a third perspective, corresponding to the Dirac interaction picture. In doing so, we assemble a list of tools from category theory which will allow us to axiomatize quantum field theories.