Quantum Field Theory notes

Although there are many phenomenal texts covering the wonderful world of quantum field theory, as a beginning learner, I found myself lost at times attempting to piece together the missing mathematical details which would in turn prevent me from understanding the theoretical underpinning of the physics at play. Luckily, our university’s professor of the subject (Michael Luke, U of T) constructed a wonderful set of course notes (primarily drawn upon the notes of Sidney Coleman’s lectures) not only compiling the great insights from himself and various authors of the subject but also demonstrating his expert digestion of the material so as to provide a clear introduction to quantum field theory suitable for graduate students and advanced undergraduate students. Ironically, however, the condensing of material for conciseness and clarity at times can appear to lack detail, at least for those at the level of an undergraduate student, including myself.

The set of notes published above are simply my own expansion of his notes with some of the various mathematical details filled in, as well as some comments and examples from other works. This is best used in conjunction with Michael Luke's aforementioned course notes and is not meant to serve as primary reference material. This project was only possible due to the rarely-found luxury of time I had prior to taking the course, as the presentation of the subject at an introductory level is typically dense and naturally coincides with the workload of taking other advanced physics courses. The presentation is raw, including various side-remarks and questions regarding the topic of concern, however I attempted to keep the writing as organised and detailed as possible as the notes progressed to make them accessible to readers outside of myself.

I hope that this project is helpful in your own journey to understanding this material and possibly improving on the field itself.

Kitaev chain model

This (small) set of notes is motivated by my summer 2023 research project in topological quantum matter. Although the contents are not conceptually enlightening, some of the calculations I included do not appear to be immediately available online.

QFT problems with solutions

An assortment of QFT problems and my own solutions. These are typed and thus more accessible than the notes. I hope that these solutions can provide both some insight into working through some of the tedious math that QFT often involves and joy in your journey of problem solving. Please feel free to email me if you see any typos or errors.