## Archive of posts in 2024

### Some understanding of Grassmann numbers out of intuition

I was briefly introduced to Grassmann numbers when I studied quantum field theory. I then had the natural question of how we can formally define them. In this article, I went with my intuition and tried to answer this question.

- Categories: math
- Tags: quantum field theory, linear algebra, abstract algebra

### The notational convenience of imaginary time in the derivation of the metric in PoincarĂ© coordinates

In general relativity, people usually choose one of the two major metric signatures. However, in certain cases, the imaginary time convention can be more convenient. Here is one of such cases: the derivation of the metric in PoincarĂ© coordinates for the anti-de Sitter space.

- Categories: physics
- Tags: general relativity, ads space

### The smallest wave packet in the lowest Landau level

The smallest wave packet in the lowest Landau level exists, and is a Gaussian wave packet. This turns out to be related to the coherent state of the harmonic oscillator.

- Categories: physics
- Tags: quantum mechanics, condensed matter physics

### Regularizing the partition function of a hydrogen atom

The partition function of a hydrogen atom diverges (only considering bound states). However, we can regularize it to get finite answers. Different regularizations give the same result. They largely agree with the physical arguments for the case of the hydrogen atom at room or cold temperature, but this should be considered a mere coincidence. The results from regularized partition functions cannot generally be trusted.

- Categories: physics
- Tags: statistical mechanics, complex, regularization, long paper

### Letting people know when you are asleep

While you are asleep, indicate that on your Discord and GitHub user status.

### Using nmcli to connect to eduroam in UCSB

Use nmcli to connect to eduroam in UCSB without using the configuration assistant tool provided by eduroam.