I was hoping someone could help me with a seeming paradox involving the Dirac equation. I have taken a non-relativistic QM course, but am new to relativistic theory.(adsbygoogle = window.adsbygoogle || []).push({});

The Dirac equation is (following Shankar)

[tex]i\frac{\partial}{\partial t}\psi = H\psi[/tex]

where

[tex]H = \vec{\alpha}\cdot \vec{p} + \beta m[/tex]

([tex]\psi[/tex] is a four component wavefunction and the alphas and beta are 4 by 4 matrices with constant entries)

It seems to me that any alpha matrix (or almost any other 4 by 4 matrix made up of constants) commutes with [tex]\partial/\partial t[/tex], but not with the hamiltonian [tex]H[/tex]. How can this be true? If [tex]\left[\vec{\alpha},H\right] \neq 0[/tex] and [tex]H = i \left(\partial/\partial t\right)[/tex] how can [tex]\left[\vec{\alpha},\partial/\partial t\right]=0[/tex] ? What am I missing?

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# Question about Dirac equation

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