1. Jul 28, 2009

### ginda770

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.

The Dirac equation is (following Shankar)

$$i\frac{\partial}{\partial t}\psi = H\psi$$

where

$$H = \vec{\alpha}\cdot \vec{p} + \beta m$$

($$\psi$$ 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 $$\partial/\partial t$$, but not with the hamiltonian $$H$$. How can this be true? If $$\left[\vec{\alpha},H\right] \neq 0$$ and $$H = i \left(\partial/\partial t\right)$$ how can $$\left[\vec{\alpha},\partial/\partial t\right]=0$$ ? What am I missing?

Last edited: Jul 28, 2009
2. Jul 28, 2009

### ginda770

Never mind, I figured it out. Stupid question. :tongue: