## Tuesday, March 1, 2011

### Obviously...

I was goofing around on the internet and somehow ended up in the dark, murky world of ultra-technical quantum mechanics/particle physics/mathematics articles on wikipedia.

The article was called Renormalization Group. Don't ask me what it means because I clearly have NO FRICKIN' CLUE. This ain't Kansas anymore.

These technical articles are usually accompanied by an endless stream of very intimidating equations that are just packed with symbols and arcane operations. But something caught my eye. Well, take a look at it:

For any positive Λ′ less than Λ, define SΛ′ (a functional over field configurations φ whose Fourier transform has momentum support within $p^2 \leq \Lambda'^2$) as
$\exp\left(-S_{\Lambda'}[\phi]\right)\ \stackrel{\mathrm{def}}{=}\ \int_{\Lambda' \leq p \leq \Lambda} \mathcal{D}\phi \exp\left[-S_\Lambda[\phi]\right].$
Obviously,
 $Z=\int_{p^2\leq \Lambda'^2}\mathcal{D}\phi \exp\left[-S_{\Lambda'}[\phi]\right].$ Obviously, the obviousness of Z is obvious...

Duhhhhh, right? I mean how can you not know what Z is? Quite obviously, Z equals all that. Looks like someone chewed up a bunch of variables and puked them out.