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Void Filler

There is a game called Nihilumbra: You are born from the void, and the void keeps chasing you, trying to engulf you. To live, you travel, you learn all kinds of "colors" as tools to fight back. After a long journey, however, the void still catches you. You are in despair. Unexpectedly, however, the void expels you - all those colors that you collected during your journey have filled your void inside. You are no longer empty. You are no longer part of the void.

You are free at last.

But that's not the end. The world has been destroyed. That will prevail in your conscience unless you fix it. 

I like this game a lot. I had always been empty since childhood. “从童年起,我便独自一人照顾着,历代的星辰。” That emptiness reached its maximum during my undergraduate study. I wouldn't have felt sorry at all, had I died at some random accident. Well, yes, there were people who loved me, there were interesting things that were nice to experience, the world was in general good. But I had no passion for anything.

Not until I finally made my way to physics.

But that's not the end. I was and still am lacking way too much knowledge. I hope to use the rest of my life to fill this new, lovely, adorable void. 

I can never fail - at least I can fill a very small part of it.


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目录 一、工作 1. 无情的事实 2. 研究 3. 角色转换 二、生活 1. 作为母亲 2. 作为妻女 3. 作为朋友和自己 三、其他感想 1. 钱财 2. 海内与海外 3. 结尾必然要盲目乐观

Basics: dimensional analysis

I decide to begin writing some back-of-the-envelope stuff in this blog; mostly very basic things. Consider Dirac fermion coupled to $U(1)$ field. $$\mathcal{L}=\bar{\psi}\gamma^\mu (\partial_\mu-iA_\mu) \psi - \frac{1}{e^2} F_{\mu\nu}F^{\mu\nu}. $$ In d spacetime dimensions, the first part in the kinetic term implies $[\partial]+2[\psi]=d$, leading to $[\psi]=(d-1)/2$. The second part leads to $2[\psi]+[A]=d$. Plugging in the value for $[\psi]$, we have $[A]=1$, then $[F]=2$. Using this and plug back in the Maxwell term $2[F]-[e^2]=d$, we arrive at $[e^2]=4-d$. When we are in 3+1d, the gauge coupling is thus dimensionless. For 2+1d, the gauge coupling has dimension $[e^2]=1$, so this theory is strongly coupled in the infrared. Also, the potential energy between two charges increases logarithmically with respect to the distance between them, which is a very mild form of confinement. References:  [1] David Tong, Lectures on gauge theory, chapter 8.