On page 172 of Schwatz’s QFT book, he derives the Klein–Gordon equation from Dirac equation as following:

$$(i \not\partial +m) (i \not\partial -m)\psi=(-\frac{1}{2} \partial_\mu \partial_\nu {\gamma^\mu \gamma^\nu}-\frac{1}{2} \partial_\mu \partial_\nu [\gamma^\mu \gamma^\nu]-m^2)\psi=-(\square +m^2)\psi =0$$

How does the second term that containing commutator of gamma matrices vanish?


$\partial_\mu\partial_\nu$ is symmetric and $[\gamma_\mu,\gamma_\nu]$ is antisymmetric.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.