Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

How do we get $[\beta , L] = 0$ , where $L$= orbital angular momentum and $\beta$= matrix from Dirac equation?

share|improve this question

1 Answer 1

The matrix $\beta$ or $\gamma_0$ is just a scalar so it doesn't change under spatial rotations. More algebraically, the angular momentum matrices in the Dirac spinor representation are given by $(\gamma_i\gamma_j-\gamma_j \gamma_i)/4$ which commutes with $\gamma_0$ because there are two sign flips (each spatial $\gamma_i$ anticommutes with $\gamma_0$).

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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