Doctor of Philosophy (PhD)
At the heart of constructive quantum field theory lies reflection positivity. Through its use one may extend results for a Euclidean field theory to a relativistic theory. In this dissertation we connect functorial and constructive quantum field theories through reflection positivity. In 2014 Santosh Kandel constructed examples of $d$-dimensional functorial QFTs when $d$ is even. We define functorial reflection positivity and show that this functorial theory is a reflection positive theory. We go on to show that every reflection positive theory produces a reflection positive Hilbert space. Iterated doubles are then introduced and used as a starting point to produce a four dimensional quantum field theory. The $(0+1)$ dimensional theory is then analyzed and shown to correspond to quantum mechanics.
Grenier, Joseph W., "Reflection Positivity: A Quantum Field Theory Connection" (2019). LSU Doctoral Dissertations. 4861.