- #1
Tomer
- 202
- 0
This isn't really a homework problem, just a form of writing I don't quite understand.
The Dirac equation is: ("natural units")
[itex] (i\gamma^{\mu}\partial_{mu}-m)\Psi = 0 [/itex]
When I try to build the conjugated equation, where [itex]\bar{\Psi} := \Psi^{+}\gamma^{0}[/itex], I get:
[itex] i\partial_{\mu}\bar{\Psi}\gamma^{\mu}+m\bar{\Psi} = 0 [/itex]
Which I've then verified and it seems correct.
However, some sources show the conjugated equation in this form:
[itex]\bar{\Psi}(i\gamma^{\mu}\partial_{\mu}-m) = 0 [/itex]
Now, I know that the scalar product is an invariant, but what I don't understand, is how I can simply shove this [itex]\bar{\Psi} [/itex] to the left side of the equation... how can the operator acting on it be situated *after* it and what does it mean?
And where does that "-m" come from? I get "+m" and so did other sources I saw...
I'm sorry if this question is dumb - this whole thing is rather new to me.
Thanks a lot!
Tomer.
The Dirac equation is: ("natural units")
[itex] (i\gamma^{\mu}\partial_{mu}-m)\Psi = 0 [/itex]
When I try to build the conjugated equation, where [itex]\bar{\Psi} := \Psi^{+}\gamma^{0}[/itex], I get:
[itex] i\partial_{\mu}\bar{\Psi}\gamma^{\mu}+m\bar{\Psi} = 0 [/itex]
Which I've then verified and it seems correct.
However, some sources show the conjugated equation in this form:
[itex]\bar{\Psi}(i\gamma^{\mu}\partial_{\mu}-m) = 0 [/itex]
Now, I know that the scalar product is an invariant, but what I don't understand, is how I can simply shove this [itex]\bar{\Psi} [/itex] to the left side of the equation... how can the operator acting on it be situated *after* it and what does it mean?
And where does that "-m" come from? I get "+m" and so did other sources I saw...
I'm sorry if this question is dumb - this whole thing is rather new to me.
Thanks a lot!
Tomer.