Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dirac eqaution

  1. Mar 19, 2013 #1
    Just to clarify in the dirac equation [itex] (i\gamma^{\mu}\partial_{\mu} -m)\psi=0 [/itex]

    Is it equal to [itex] (-i\gamma^{0}\partial_{0}+i\gamma^{i}\partial_{i} -m)\psi=0 [/itex] in (-,++++) notation?
  2. jcsd
  3. Mar 19, 2013 #2


    User Avatar
    Science Advisor

    No, for a repeated index with one index up and one index down, just sum:

    γμμ = γ00 + γ11 + γ22 + γ33

    You only need to use the Minkowski metric if both indices are up, or both indices down:

    ημνγμν = - γ00 + γ11 + γ22 + γ33

    or ημνγμν = - γ00 + γ11 + γ22 + γ33
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook