Studying the basics of spin-$\frac{1}{2}$ QFT, I encountered the gamma matrices. One important property is $(\gamma^5)^\dagger=\gamma^5$, the hermicity of $\gamma^5$. After some searching, I stumbled upon this interesting Phys.SE answer to an earlier question on this forum. Specifically, I am int...
Reviewing some basic special relativity, and I stumbled upon this problem:
From the definition of the proper time:
$$c^2d\tau^2=c^2dt^2-dx^2$$
I was able to derive the time dilation formula by using $x=vt$:
$$c^2d\tau^2=c^2dt^2-v^2dt^2=c^2dt^2\left(1-\frac{v^2}{c^2}\right)\rightarrow d\tau = dt\...
I'm currently studying Carroll's GR book Spacetime & Geometry, and ran into some trouble understanding the text. When discussing Killing vectors, Carroll mentions that one can derive
$$K^{\lambda}\nabla_{\lambda}R=0$$
That is, the directional derivative of the Ricci scalar along a Killing vector ...
In inflationary theory, many papers start off by making the slow-roll approximation, on which many things depend. This approximation is usually presented by requiring that two 'slow-roll parameters' are small:
$$\epsilon_V\equiv\frac{1}{16\pi G}\left(\frac{V'}{V}\right)^2 \ll 1$$
$$|\eta_V|\equiv...
In Wikipedia, spacetime intervals are presented explicitly under the heading "Spacetime intervals in flat space"; apparently including a presentation of spacetime intervals for (all) pairs of events in flat spacetime.
Now, certainly spacetimes may be considered such that none of their subsets c...
