Mathematical Aspects of Classical and Quantum Field Theory

This lecture was given by Dr. Schiavina of ETH Zürich and Dr. Canepa of UZH in the fall semester of 2021. It gives an extended introduction to the mathematical background of Classical and Quantum Field Theory.

The lecture paints the field as both a mathematical theory motivated by physical ideas and a physical theory requiring deep mathematical understanding.

While I am working on mostly unvetted and entirely unofficial lecture notes, I'd really recommend reading at least the introduction of Renormalization and Effective Field Theory by Kevin Costello which has been a great help in understanding the harder proofs and concepts.