enter image description here

This is an exercise from Peskin&Schroeder's book. The exercise requires to show that $\textbf{J+}$ and $\textbf{J-}$ commute with each other. What is the exact meaning of commutation between operators that are the form of vectors? Do I have to just show that $[\textbf{J+}^i, \textbf{J-}^i]=0$? Or do I have to show that $[\textbf{J+}^i, \textbf{J-}^j]=0$? I am confused...

  • $\begingroup$ Are you confusing 'vector operator' (i.e. an operator that acts on vectors) with 'operator that is a vector'? $\endgroup$ – Acccumulation Mar 15 '18 at 15:17
  • $\begingroup$ I mean the latter. $\endgroup$ – Keith Mar 15 '18 at 15:18
  • 1
    $\begingroup$ You have to show that each component of the first vector commutes with each component of the second. $\endgroup$ – lcv Mar 18 '20 at 21:08

in this specific case you have to show that $$[J_+^i,J_-^j]=0$$ meaning that every component commutes with every component.

  • $\begingroup$ Only in this specific case? How about general cases? $\endgroup$ – Keith Mar 15 '18 at 15:13
  • $\begingroup$ The above relation is more general than $[J_+^i,J_-^i]=0$. $\endgroup$ – Ozz Mar 15 '18 at 15:15

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.