2Gou - June 28, 2017

2Gou - June 28, 2017

Nice to meet you!

Hello World,

This is 2Gou's sandbox in Wikidot.

Firstly, I intend to learn about the equations. It seems that this site is compatible with LaTeX, great. We have $(T_A)_\mu^{\ \nu}(x)={\dfrac{d}{d\lambda}}\vert_{\lambda=0}\ (\Lambda_A)_\mu^{\ \nu}(\lambda)$ by

(1)
\begin{split} T_\mu^{\ \nu}(x) &\in \mathfrak{spin}^*(1,3)\cong\mathfrak{spin}(1,3)\cong \overline{\mathfrak{so}}(1,3)\\ &\cong \mathfrak{spin}(3)\oplus \mathfrak{spin}(3)\\ &\cong \mathfrak{su}(2)\langle\text{spin}\rangle\oplus \mathfrak{su}(2)\langle\text{boost}\rangle \end{split}

and $\gamma_\alpha\times\gamma_\beta = \dfrac{1}{2}(\gamma_\alpha\gamma_\beta-\gamma_\beta\gamma_\alpha)=\gamma_{\alpha\beta}\in \mathfrak{Cl}^2(1,3)\cong \mathfrak{spin}(1,3)$.

Okay, above shows the practice today. I like it.

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