The Dirac equation and its conjugate

  • Thread starter Tomer
  • Start date
  • #1
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.
 

Answers and Replies

Related Threads on The Dirac equation and its conjugate

Replies
0
Views
1K
  • Last Post
Replies
4
Views
2K
Replies
5
Views
4K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
744
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
6K
Replies
3
Views
1K
Replies
5
Views
854
  • Last Post
Replies
1
Views
2K
Top