Changing Font size on Blogger

Step 1: Login to Blogger.
Step 2: Click on Drop down as shown and select "Template"



Step 3: Click on Customize.



Step 4: Click on "Advanced"


Step 5: Select desired Font and Font Size.


Step 6: Click on "Apply to Blog" on top right hand side of the page to apply your settings.

Georgi Lie Algebras Chapter 2 Solutions

==Problem 2A==
Find all components of matrix $e^{i\alpha A}$ where $A$ is $$A=\left(\begin{array}{ccccc}0& & 0& & 1\\ 0& & 0& & 0\\ 1& & 0& & 0\end{array}\right)$$

==Solution==
Simply exp will yield, $$\left(\begin{array}{rrr}\frac{1}{2}(e^{\left(2iy\right)}+1)e^{(-iy)}& 0& \frac{1}{2}(e^{\left(2iy\right)}-1)e^{(-iy)}\\ 0& 1& 0\\ \frac{1}{2}(e^{\left(2iy\right)}-1)e^{(-iy)}& 0& \frac{1}{2}(e^{\left(2iy\right)}+1)e^{(-iy)}\end{array}\right)$$ Then applying Demovire's theorem, one gets, $$\left(\begin{array}{rrr}\frac{1}{2}(\cos \left(2y\right)+i\sin \left(2y\right)+1)(\cos \left(y\right)-i\sin \left(y\right))& 0& \frac{1}{2}(\cos \left(2y\right)+i\sin \left(2y\right)-1)(\cos \left(y\right)-i\sin \left(y\right))\\ 0& 1& 0\\ \frac{1}{2}(\cos \left(2y\right)+i\sin \left(2y\right)-1)(\cos \left(y\right)-i\sin \left(y\right))& 0& \frac{1}{2}(\cos \left(2y\right)+i\sin \left(2y\right)+1)(\cos \left(y\right)-i\sin \left(y\right))\end{array}\right)$$

==Problem 2B==
If $[A,B]=B$, calculate $$e^{i\alpha A}B{e}^{-i\alpha A}$$ Using equation $2.44$, and setting $Y=-Z$, we get $$\begin{array}{r}RHS=X-i[-Z,X]-\frac{1}{2}[-Z,[-Z,X]]+\cdots \\ & & =& & X-i[X,Z]-1/2[[X,Z],Z]+\cdots \end{array}$$ Applying this to equation in our problem, $$\begin{array}{r}{e}^{i\alpha A}B{e}^{-i\alpha A}=B-i\alpha [B,A]-\frac{1}{2}{\alpha }^2[[B,A],A]+\cdots \\ =B+i\alpha B-\frac{1}{2}{\alpha }^2[B,A]+\cdots \\ =B+i\alpha B-\frac{1}{2}{\alpha }^{2}B+\cdots \\ =B{e}^{-i\alpha }\end{array}$$

How to configure blogger for MathJax

Step 1: Login to Blogger
Step 2: Select "Layout" from the dropdownlist.


Step 3:Click Edit in the Cross Column.

Step 4: Copy and paste the following code.

<script type="text/x-mathjax-config">
  MathJax.Hub.Config({
    extensions: ["tex2jax.js"],
    jax: ["input/TeX", "output/HTML-CSS"],
    tex2jax: {
      inlineMath: [ ['$','$'], ["\(","\)"] ],
      displayMath: [ ['$${}^{\prime }{,}^{\prime }$$'], ["\[","\]"] ],
      processEscapes: true
    },
    "HTML-CSS": { availableFonts: ["TeX"] }
  });
</script>


<script src='https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML'></script>

Step 5: Click Save.


Step 6: Start using LaTex in your blog. The minimal configuration as noted above won't support all features. Check out the MathJax documentation by clicking link - MathJax Docs
Step 7: Publish and Prosper!