Alberto Nicolis

If you are a physics major, you HAVE to take this class. Pros: Alberto is by far the best lecturer I have had in the math and physics departments. He is clearly incredibly intelligent and has such a solid grasp on foundational concepts that he is able to effectively communicate in concise and simple explanations to an undergrad level. I feel frustrated that I haven't had a class like this sooner because almost every topic (hilbert spaces, operator algebra, distributions, complex analysis, fourier series) I have been exposed to but never understood (mostly bc physics profs don't like to explain math concepts). I think every physics major should definitely take this class. Cons: There is no syllabus at all and the topics feel a little disconnected. Alberto tends to lecture pretty quick, he usually tries to go over as many of the main ideas and points instead of mulling over the details of a specific example

representation theory, spinors, fermion and boson lagrangian and interactions, standard model construction

Linear algebra, operator theory, Hilbert spaces, distribution theory, fourier transforms, complex analysis, Green's functions, all from the point of view of physics and physics applications

Finally a good explanation for the motivation behind the non-Abelian gauge theories. Although

some intro abstract algebra, spectral decomposition/ diagonalization of operators, hermitian operators, Hilbert spaces, functionals, distributions, Fourier transforms, complex analysis (contour integrals, branch cuts, green's functions)

Lots of useful math techniques for Physics

We covered QFT for spinor fields and gauge fields (abelian and non-abelian). Namely, we discussed real-life QFTs including QED, QCD, and the electroweak sector of the Standard Model (i.e. the Higgs mechanism). We also looked at some concrete examples of renormalization of realistic theories and what their beta functions look like (ex. asymptotic freedom). The beginning of the course included a review of the general theory of QFT from the path integral perspective and a number of theory topics like the optical theorem.

Vector spaces, operators, diagonalization, distributions, complex analysis, Fourier transforms, etc...

Linear operators, complex analysis, and fourier transforms

Would recommend to everyone who is at least somewhat interested in the high-energy physics. I did not know anything about particle physics and still, somehow, never felt out of touch during the class. 1 Columbia University: Arts & Sciences Fall 2022 Course: PHYSGR8048_001_2022_3-QUANTUMFIELDTHEORYII : PHYSGR8048_001_2022_3 - QUANTUM FIELD THEORY II Instructor: Alberto Nicolis