Timeline for Representation under which Pauli matrices transform
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 15, 2020 at 19:21 | comment | added | Prahar | @SamapanBhadury - see comment above. | |
| Oct 15, 2020 at 19:21 | comment | added | Prahar | Let us continue this discussion in chat. | |
| Oct 15, 2020 at 19:21 | comment | added | Samapan Bhadury | can you kindly explain this statement or direct me to a reference. | |
| Oct 15, 2020 at 19:17 | comment | added | Prahar | @SamapanBhadury No no. I mean that $\delta^\alpha_\beta$ is a Lorentz invariant tensor, but $\delta_{\alpha\beta}$ is NOT and we are only allowed to use Lorentz invariant tensors since the LHS is a Lorentz invariant tensor. | |
| Oct 15, 2020 at 19:16 | comment | added | Samapan Bhadury | you mean to say $\delta^\alpha_\beta$ does not exist? | |
| Oct 15, 2020 at 19:10 | comment | added | Prahar | @SamapanBhadury - $\delta$ has one upper index and one lower index. The LHS has all four indices lowered. | |
| Oct 15, 2020 at 19:09 | comment | added | Samapan Bhadury | why not $\delta_{\alpha\beta} \delta{\gamma\delta}$? Why can't we construct with such $\delta$-functions? | |
| Oct 15, 2020 at 18:54 | comment | added | Prahar | @SamapanBhadury - (1) what else could it be? I've already written down all the Lorentz invariant quantities for you. What remains is to construct something from those but with the right index structure. (2) ya, that sounds right. my metric convention is (-+++) | |
| Oct 15, 2020 at 18:52 | comment | added | Samapan Bhadury | There is a difference of sign with your proof and the one of Peskin. Is it due to different metric choices? | |
| Oct 15, 2020 at 18:50 | comment | added | Samapan Bhadury | @Pahar The one thing I don't understand is, why the only Lorentz invariant quantity possible is $\varepsilon_{\alpha \gamma} \varepsilon_{\dot{\beta} \dot{\delta}}$? | |
| Jan 18, 2020 at 19:22 | history | answered | Prahar | CC BY-SA 4.0 |