Given the Hamiltonian [itex]H = \vec{\alpha} \cdot \vec{p} c + \beta mc^2[/itex],(adsbygoogle = window.adsbygoogle || []).push({});

How should one interpret the commutator [itex][\vec{x}, H][/itex] which is supposedly related to the velocity of the Dirac particle? [itex]\vec{x}[/itex] is a 3-vector whereas H is a vector so how do we commute them. Is some sort of tensor product in order? ie

[itex][\vec{x}, H] = x_i H_{jk} - H_{jk}x_i[/itex]?

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# Commutation relations in relativistic quantum theory

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