## About Physics --- Before July

As was mentioned in an early post Goals for 2019, I had worked on several courses but not finished them all. Here I will list courses that I have finished.

*Group Theory in a Nutshell for Physicists*by Antony Zee. I finished Part I ~ VI in April.*8.06x Applications of Quantum Mechanics*by Barton Zwiebach. This is an excellent course provided by MIT in edX. I have written a term paper for this course explaining the notion of a single photon. We know from high school physics that photon sometimes behaves like particles and sometimes behaves like waves. In this paper, I introduce a framework where this wave-particle duality will arise naturally.*18.6501x Fundamental of Statistics*. This course exposes some basic statistics idea to me. I passed the course but didn’t take its final exam.*Complex Analysis with Physical Applications*by two Russian physicists: Prof. Yaroslav Rodionov and Prof. Konstantin Tikhonov. I only finished 7 out of all 9 units. I will definitely do this course again when it reruns in the future.*Einstein Gravity in a Nutshell*by Antony Zee. I only finished first 6 parts in the book, seeing how Einstein’s Field Equation is derived. I will reread this book and finish all of it in the future.

## About Physics --- July and August

I attended a workshop called Computational Approaches to Quantum Many-body Problems(CAQMP) organized by my supervisor in Japan. This is the first time I’ve ever attending a physics workshop. I just want to get myself familiar with what I will work on later. I didn’t understand most of the talks in this workshop. Most people attending this workshop were professors or postdoctors. However, I did meet a few interesting friends during this workshop.

I also spend one week or two to work on the remaining problems in the project with Jim. It is about the form of the translational operator in spherical coordinate, since we need it to calculate the wavefunction in coordinate space representation using operator methods.

## About Physics --September to December

I arrived in Japan on maybe 10th September, and spent about 10 days to find my own apartments and settled down. I started working on Physics in October.

In The University of Tokyo, I took the following three courses this semester:

*Elementary Particle Physics*. It was not a very interesting course. It covers the contents in Griffiths’s elementary particle book. I think I will need to work on Griffiths book later on my own if I really want to learn elementary particle physics.*Quantum Field Theory II*. This course mainly covers quantization of electromagnetic (EM) fields and also Dirac fields. The two can be put together using minimal coupling and the gauge principle. We then got the famous Quantum Electrodynamics (QED). In this course, we mainly use canonical quantization method to quantize both Dirac fields and EM fields. It also introduces some non-abelian field. I can follow the math but haven’t understood much the physics. The course also covers the renormalization to deal with the infinities in loop corrects very briefly.*Information Compression in Computational Science*by Prof. Yamaji and Prof. Okubo. This is an interesting course, mainly dealing with some applications of computational linear algebra techniques. The course has a public website on GitHub. It mainly covers low-rank approximations techniques of matrices, sparse modeling, etc.

I also read a few textbooks and did one online course:

*Quantum Field Theory in a Nutshell*by Antony Zee. I certainly didn’t finish this book, only read some chapters in Part I and Part II. This is certainly a very interesting book. It gives a rather nice treatment of path integrals for field theory in Part I.**I will definitely work through this book carefully one day (maybe in 2021)**.*Statistical Physics of Fields*by Mehran Kardar. This book has a corresponding course on MIT/OCW with course number 8.334. The book is basically a detailed lecture notes for Kardar’s lectures. He treats Landau-Ginzberg model in great details, starting with mean-field approximation, then moving on to consider the fluctuation around the saddle-point solution. There will be an infrared divergence for systems in low space dimensions. Kardar then introduces renormalization group approach to deal with this problem. Various lattice models and techniques like high and low temperature expansion are also discussed. This book treats everything using classical picture. No quantum at all. This is a nice book!- A course on quantum optics: Quantum Optics 1 : Single Photons provided by École Polytechnique and lectured by Alain Aspect and Michel Bruce. This course is recommended by Jim and is closed related to my 8.06x term paper.

My research topic is related to real-space renormalization group using the so-called tensor network technique. In order to get a big picture about tensor network states and many-body computational physics, I went through lectures of a course in PSI with the name, Explorations in Condensed Matter, provided by Prof. Guifre Vidal. It is a three-week course. In first week, Prof. Vidal first introduces how to use exact diagonalization to find the spectrum of a system. Free fermion formalism is also introduced. In second week, he talks about structure of entanglement in ground state of many-body systems, the so-called area law. In third week, he then introduces various tensor network ansatz, which is carefully designed to have the desirable entanglement structure. This is an excellent course. Prof. Vidal explains everything like crystal clear.

As for my research topic, I had been mainly learning various concepts and techniques during those three months. I first need to get myself familiar the simplest system in many-particle physics, Ising Model. First 1D, and then 2D. Then I learned two tensor network renormalization group(TNRG) method, TRG and TNR, and also two ways to extract scaling dimensions under TNRG framework.

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