Let's say we have a ladder or length $L$ and height $b$ against a wall, leaning at angle $\theta$. There are two masses of mass $m$ on each end (one against the wall, and on the floor). Where $a$ is the length of the $x$ component of the ladder. In order to solve for their velocities at $t=0$, we...

The Darwin term can be obtained from the low energy approximation ($|p|^2/m^2<<1$) of the Dirac equation of the electron in a central field. An elegant way to perform this task is by means of the Foldy-Wouthuysen Transformation. The same approximation leads also to the other terms detected in the...

How do you show that ${\gamma^5}^\dagger = \gamma^5$, where: $$ \gamma^5 := i\gamma^0 \gamma^1 \gamma^2 \gamma^3$$ and we know that: $$ \left\{\gamma^\mu,\,\gamma^\nu\right\}=2\eta^{\mu\nu}\mathbb{1}~$$ Note: I would like to show this using only these two relations, and in particular, not using ...