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Among all the experiments that I did for schoolwork, the Cavendish experiment is the most tedious one. I mean, the fact that I can measure such a small gravitational force is very amazing, but the steps that an experimenter need to take are so boring that I even feel that I wasted a part of the course of my life in this.
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Articles
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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
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The notational convenience of imaginary time in the derivation of the metric in Poincaré 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 Poincaré coordinates for the anti-de Sitter space.
- Categories: physics
- Tags: general relativity, ads space
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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
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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
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Letting people know when you are asleep
While you are asleep, indicate that on your Discord and GitHub user status.
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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.
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The duality between two plane trajectories related by a conformal map
The conformal map transforms the trajectory with energy in potential into the trajectory with energy in potential . I will prove this beautiful result and show some implications of it.
- Categories: physics
- Tags: complex, classical mechanics, canonical transformation, kepler problem, mathematical physics, vector analysis, long paper
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Embed the latest Mastodon post in my website
I show the latest Mastodon post in my website hosted on GitHub Pages, and it does not require JavaScript on the client side. How do I do that?
- Categories: update
- Tags: web, jekyll, selfhosting
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Rotational symmetry of plane lattices as a simple example of algebraic number theory
For a plane lattice, there is only a finite number of different rotational symmetries that are compatible with the discrete translational symmetry. For example, the 5-fold rotational symmetry is not one of them. Why is that? It turns out that whether an -fold symmetry is compatible with translational symmetry is the same as whether .
- Categories: math
- Tags: complex, condensed matter physics, algebraic number theory, lattice, mathematical physics
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I restructured my blog
If you have not noticed, the equations on my blog are now rendered server-side. This change makes it possible for those who turn off JavaScript on their browsers to see the equations. I also updated the theme from Minima v2 to Minima v3.
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