Timeline for Hermitian Adjoint of Dirac Equation vs Dirac Lagrangian
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 1, 2020 at 20:24 | vote | accept | Carlo | ||
| May 1, 2020 at 20:23 | comment | added | Qmechanic♦ | It seems you understand correctly. | |
| May 1, 2020 at 20:04 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
added 3 characters in body
|
| May 1, 2020 at 19:45 | comment | added | Carlo | If I understood that correctly, this operation does the conjugation only wrt Dirac indices: $$ \mathcal{L}_D^\dagger = \Psi^\dagger(-i {\gamma^\dagger}^\mu \overleftarrow{\partial_\mu} - m)\gamma^0 \Psi = \dots = \bar\Psi (-i\gamma^\mu \overleftarrow{\partial_\mu} - m) \Psi $$ and then, after an integration by part, we find the original $\mathcal{L}_D$ with the right (no pun intended) verse of the derivative? And the reason why we don't integrate by part in the adjoint Dirac equation is that we want the derivative to act on the adjoint spinor, which is on the left? | |
| May 1, 2020 at 18:20 | history | answered | Qmechanic♦ | CC BY-SA 4.0 |