Title: Today’s pieces

Date: 2013-01-29 23:28:06

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Time was really limited! Especially when you were sitting in front of a computer.

Today I was trying to read Prof. Zhou’s article Local Mirror Symmetry for One-Legged Topological Vertex |arXiv:0910.4320v2. However, after few minutes, I started to digress. I was unfamiliar with Quantum field theory. So I went to google it. What I had found was an article on Quantum field theory.

Basically, Quantum field theory deals with quantum mechanics in the context of relativities. Since according to the theory of relativity, the number of particles will not be conserved. Namely, particles can be created or annihilated.

Then I was stopped at the concept of Legendre transform. I found an arXiv article tell us how to learn Legendre transform in a mathematical way. The article is in the physics education section, named Making Sense of Legendre transform | arXiv:0806.1147v2. From this paper, I’ve learned how to memorize the form of Legendre transform. It was actually forming in a very symmetric way: Suppose we have a function (L(x)), which is a convex (means the second derivative is always positive). Then the goal of Legendre transform is to express (L(x)) in terms of (s), where (s) is a new variable defined as [s = \frac{\partial L}{\partial x}]. Notice (s) is a monotone function of (x), so we can find the inverse function of (x) in terms of (s) with no difficulties. By using it, we can change (L) to a function of (s). But we do not want to do that, we do the following: Let (H(s)) is the transformed function. Then (H(s)) and (L(x)) are related by [H(s)+L(x) = s;x.] See? It is so symmetric. Obviously, this is the very first insight in this paper. But this is the most impressive part for me so far.

Then I saw a paper in Science website. It is about music and math. The author interprete chords and notes by points in Euclidian space. Since some different chords may have some similar voice, the author identified this. Then we are considering chords by points in some orbifold. And the author somehow discussed the distance in this orbifold.

The last thing about today was about the famous book Surreal numbers written by Knuth. It is a famous but somehow length book. So someone wrote a short introduction to this book, called Surreal numbers–An introduction. I may read this shorter version sometime.

So, time is short, I was not finish any of this readings. So I write them down to memorize these wonderful things I can do in the future!

Good night, world!! ^^