Does our editor's example equation need to be changed to something else?

Question

Currently, when one clicks the \(\TeX\) button while writing a post, one is presented with the example  of a solution to a second-order polynomial equation. 

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

PolarKernel asked on the thread; Public Beta Feature Requests whether we want a more physics-ish or high-level example equation instead.  

I see that we could have one of the following kinds of example equation:  

• Functional ones; common examples, like our current example equation.  
• Physics-ish fun ones, say, something like \(\left\langle \mathcal{T}\left\{ \exp\left(\int \mathrm{d}x^D J_{4D}(x)\mathcal{O}(x)\right) \right\} \right\rangle_{\mathrm{CFT}} = Z_{\mathrm{AdS}}\left[\lim_{\mathrm{boundary}} J \omega^{\Delta-D+n } = J_{4D}\right]\) (from AdS/CFT) 
• Commonly used, useful equations, e.g. Dirac Field Lagrangian, or Polyakov Action, or something like that.  
• Solely to show some of the features of MathJax; e.g. \( {\mathcal{L}} = \left[ {\begin{array}{*{20}{c}}{2k\sum\limits_\pi ^\infty {{\Gamma ^{\int {\rm{d}} {\mathbb{F}}}}} }&0\\0&1\end{array}} \right] \)
• Something creative and fun; here's a dumb thing I thought of: \(\bf{{MaThJaX}^{-1}\lvert p\hbar0\rangle}=0\).  

Commonly used equations may be advantageous because they may reduce equation-typesetting time. But with different conventions used, etc., it may not turn out to be very useful eventually.  

Physics-ish equations may help ward off low-level questions, and give the message that "this is not the place for your question", which is good. 

The creative and fun things are useless but fun.  

So, please propose example equations, or say "I'd rather stick to our current, functional, example equation." if you prefer.  

Comments

Haha, the one from AdS/CFT is cool :-)

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@Dilaton I have proposed it below.  

Answer 1

I propose that we use this equation: 

\(\left\langle \mathcal{T}\left\{ \exp\left(\int \mathrm{d}x^D J_{4D}(x)\mathcal{O}(x)\right) \right\} \right\rangle_{\mathrm{CFT}} = Z_{\mathrm{AdS}}\left[\lim_{\mathrm{boundary}} J \omega^{\Delta-D+n } = J_{4D}\right]\)