Math & Physics Lectures

Quantum Field Theory Research

Miscellaneous

**Podcast**

My podcast The Cartesian Cafe where an expert guest and I map out mathematical and scientific subjects in detail.

**Math & Physics Lectures**

Mathematics and physics videos for a general audience looking to get into the technical details. My setup.

**Quantum Field Theory Research**

Videos I created in 2016 on my academic research in quantum field theory at the time using whiteboard animation.

**The Perturbative Approach to Path Integrals**

**Synopsis:** In this video, I highlight the confusion and shortcomings of standard (textbook) explanations of the perturbative approach to path integrals in quantum field theory, that in my experience, still exists widely among mathematicians and physicists today. The resolution is through a proper understanding of the relationship between integration and what I call the Wick expansion, which is the formal algebraic operation underlying the method of Feynman diagrams.

**Quantum Yang-Mills Theory in Two Dimensions**

**Synopsis:** Traditional mathematical subjects enjoy having their foundations provided “ready-made”. This is quite the opposite situation in the study of quantum field theory, where many approaches and constructions exist but without a clear consensus as to the relationships among them. One of the major goals of the subject is to rigorously understand nonperturbative quantum field theories, as opposed to their perturbative (and thus formal) counterparts in the sense described above. To my surprise, a rigorous mathematical study of the relationship between these distinct nonperturbative and perturbative formulations in the setting of gauge theories has been overlooked. This inspired my original investigation of such issues in the context of two-dimensional Yang-Mills theory, since this is an exceptional case in which the exact (nonperturbative) theory is known. My findings, which build upon the work of many, establish results that reveal in detail the ways in which the exact and perturbative formulations of 2D Yang-Mills agree and differ.

**Miscellaneous**

I have hosted some interviews for Talks at Google:

**Marcus Du Sautoy**

**Sabine Hossenfelder**