1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: The Dirac equation and its conjugate

  1. Feb 23, 2012 #1
    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!

  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted