Recent content by ag_swe

Thanks, interesting paper. In fact, since {β,α_i}=0, I think one can simply swap β and α₂, which makes all gamma matrices purely imaginary.

I'm just wondering how the Majorana matrices first were found. I have only seen them immediately written down at different webpages, and never seen a derivation. Is it obvious how to transform the Dirac gamma matrices into the Majorana representation?

Homework Statement Show that the matrices \mathcal{D}_{m',m}^{(j)}=\langle j,m'|\exp(-\frac{i}{\hbar}\vec{J}\hat{n}\Phi)|j,m\rangle form a group (i.e. multiplication, inverse and identity). No idea how to even begin.

Thank you very much. Very appreciated! However, I didn't get how to find the two vector products without "looking into the future", i.e., knowing what I was looking for.

Studying in the Heisenberg picture, we have \frac{\text{d}x_i}{\text{d}t}=-\frac{\text{i}}{\hbar}[x_i,H]=\frac{1}{m}\left(p_i-\frac{q}{c}A_i\right) where the last bracket is known as the kinematic momentum \pi . Now, to find \frac{\text{d}^2{\bf{x}}}{\text{d}t^2} I do the following...