# The Dirac equation and its conjugate

1. Feb 23, 2012

### Tomer

This isn't really a homework problem, just a form of writing I don't quite understand.

The Dirac equation is: ("natural units")

$(i\gamma^{\mu}\partial_{mu}-m)\Psi = 0$

When I try to build the conjugated equation, where $\bar{\Psi} := \Psi^{+}\gamma^{0}$, I get:

$i\partial_{\mu}\bar{\Psi}\gamma^{\mu}+m\bar{\Psi} = 0$

Which I've then verified and it seems correct.

However, some sources show the conjugated equation in this form:

$\bar{\Psi}(i\gamma^{\mu}\partial_{\mu}-m) = 0$

Now, I know that the scalar product is an invariant, but what I don't understand, is how I can simply shove this $\bar{\Psi}$ 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.