Timeline for Lorentz Invariance of Weyl Lagrangian
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 17, 2022 at 3:43 | comment | added | DEEP GHOSH | Use lorentz transformation properties for R type helicity spinor and transformation for \delta_\mu. From there the lorentz invariance property would come. | |
| Jan 15, 2022 at 20:25 | comment | added | Yadeses | @asdf Have you ever figured this out? | |
| Dec 4, 2020 at 10:54 | comment | added | asdf | I'm sorry but I cannot get your point. We can include $\psi^{\dagger}_{R}\sigma^{\mu}\partial_{\mu} \psi_R$ in the Lagrangian if it is Lorentz invariant, and the author insists that it's indeed so. Why on earth is $\psi^{\dagger}_{R}\sigma^{\mu}\partial_{\mu} \psi_R$ Lorentz invariant? | |
| Dec 4, 2020 at 6:11 | comment | added | DEEP GHOSH | We need another vector that can contract with $V^{\mu}_R$ to give a scalar. Now, $\partial_{\mu} V^{\mu}$ is a total derivative, but we can use a part of it.\begin{equation}\partial_{\mu} V^{\mu} =\partial_{\mu}\psi^{\dagger}_{R}\sigma^{\mu}\psi_R + \psi^{\dagger}_{R}\sigma^{\mu}\partial_{\mu} \psi_R\end{equation} we can use either of terms in the right hand side of the equation to write down Dirac Lagrangian. | |
| Dec 2, 2020 at 17:23 | comment | added | asdf | In the Schwartz's book, the author uses the Lorentz invariance of $\psi_{R}^{\dagger} \partial_{t} \psi_{R}+\psi_{R}^{\dagger} \partial_{j} \sigma_{j} \psi_{R}$ directly to derive the Dirac Lagrangian from which the Weyl equation can be derived by taking $m\rightarrow 0$. Could you derive this from the fact that $V_R^\mu$ is a 4-vector? | |
| Dec 25, 2019 at 5:23 | history | answered | DEEP GHOSH | CC BY-SA 4.0 |