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## Homework Statement

Momentum, involving variational calculus.

[tex]\psi^{\dagger}[/tex]

[tex]\bar{\psi}[/tex]

matrices [tex](\alpha, \beta)[/tex]

## Homework Equations

[tex]i \bar{\psi} \gamma^0 = i\psi^{\dagger}[/tex]

## The Attempt at a Solution

Am I to understand, that the momentum [tex]P=i\psi^{\dagger}[/tex], concentrating on the right hand side, is really just

[tex]i \beta \bar{\psi}[/tex]

I am led to believe this since

[tex]\bar{\psi} \beta = \psi^{\dagger}[/tex]

Would I be right in saying this? If so, since the [tex]\gamma^{0}[/tex] is really just the beta matrix for the time derivatives [tex]\beta \partial_t[/tex], is this just

[tex]i \bar{\psi} \gamma^0 = \psi^{\dagger}\beta[/tex]