The lectures, by Piljin Yi, are intended to supplement regular graduate courses on quantum field theory in that no effort will be given to derivation of Feynman diagrams or to the latter’s numerous applications. We will be relying on the functional Gaussian integration via the Heat Kernel, a.k.a. Schwinger-DeWitt method, although real-time lectures themselves will perform loop computations minimally, relegating much to the very detailed lecture notes and self-study thereof. 

The goal is not to teach QFT from scratch but rather remedy some prevalent confusions and wrong impressions after the initial encounter with QFT. This includes the Noether procedure, quantization of fermions, index theorems and related mathematical backdrops, exotic aspect of continuous anomalies, odd-dimensional effective actions, and discrete anomalies. The renormalization shall be given a particular attention early on, certainly not as a collection of tricks that deal with the ultraviolet ”divergences” but rather as Wilson’s momentous insight that allows us to define the very framework of quantum field theories. Along the way, we come to the question of why the fundamental forces in our real world had to be in the form of gauge theories.  The later courses will lean heavily toward geometric and topological aspects of gauged theories, inclusive of gravity, with a view toward other corners that range from topological insulators to superstring theories. 

• Hours and Venue: Every Wednesday, 10AM~Noon, KIAS #1424 with a Zoom broadcast, beginning October 30th 2024

• Prerequisites:
1. at least one semester of quantum field theory
2. either General Relativity or graduate mathematical physics (Nakahara or Equivalent)

• Duties expected of the attendees
1. attendance on par with regular credited classes
2. critical & proof-reading of the distributed lecture notes (to remain within the class, absolutely)
3. (sporadic) group project presentations, perhaps