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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.