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

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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 $\gamma_0$).

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