Math Intuition for Quantum Mechanics & Quantum Field Theory

This course aims to mathematically motivate both Quantum Mechanics (QM) and Quantum field Theory (QFT). The first part is devoted to the most important concepts and equations of QM, whereas the second part deals with QFT.

Due to the conceptual and mathematical difficulty of these subjects, some prerequisites to this course are unavoidably required. The student should be familiar with:

1) the Fourier Series and Transform;

2) Multivariable Calculus;

3) Probability theory and random variables;

4)  Classical Physics;

5) Complex Calculus (especially residues and calculation of integrals on a contour), although this is necessary only for some parts of the course devoted to QFT;

6) Special Relativity and tensors for QFT.

Note 1: the first few prerequisites might be enough if you are interested only in the first part of the course, which is related to QM (consider that this course has tens of hours’ worth of material, you might be interested only in some parts);

Note 2: I’m more than willing to reply if you have doubts/need clarifications, or -why not- have any recommendations to improve the quality of the course.

Note 3: I’ll still keep editing the videos (for example by adding notes) to make the video-lectures as clear as possible.

The references for the part on QFT are the following:

– Quantum Field Theory, M.Srednicki

– Quantum Field Theory, Itzykson & Zuber

– QFT by Mandl & Shaw

– QFT in a nutshell, A.Zee

– QFT by Ryder, Ramand

– The Quantum Theory of Fields, S.Weinberg

– Gauge Theories in Particle Physics, Aitchison & Z.Hey