Topological Field Theories

In this lecture on The Topological Field Theories (TFTs), I will discuss the types of TFTs i.e. Schwarz type and Witten type, giving a Mathematical description of a topological field and theory with a physical example of Topological Field Theory. I will talk about the difference between Geometry and Topology, and how can one have situations that only care about the topology. To answer what does a topological field theory looks like we will consider Electromagnetic field. Discussing what role does a metric play here. We will certainly need some tools we developed in in the lecture on Differential forms. I will talk about Quantum mechanical theories and briefly on the “Renormalization” process, here we will see how one can make a theory purely topological. Finally, we will see what all of this looks like with an example of an electron in some perturbation, this is where we will first see what a Chern-Simons Theory looks like. At the end of the video we will realize how this Quantum mechanical calculation is effectively a calculation of topology.

Видео Topological Field Theories канала BasylDoesPhysics