I calculated the expectation value of the momentum of the charge-conjugated Dirac spinor and found that it was the negative of that of the Dirac spinor. Here is the calculation.(adsbygoogle = window.adsbygoogle || []).push({});

Charge conjugation operator is chosen to be [itex]C=i\gamma^0\gamma^2[/itex]. The spinor is [itex]\Psi[/itex] and its charge-conjugated spinor [itex]\Psi_C=-i\gamma^2\Psi^*[/itex].

The expectation value of the momentum of [itex]\Psi_C=-i\gamma^2\Psi^*[/itex] is given by

[itex]<\vec p>_C=\int d^3x\bar\Psi_C\vec p\Psi_C=\int d^3x\Psi^T\gamma^0\gamma^2\vec p\gamma^2\Psi^*=-[\int d^3x\bar\Psi\vec p^*\Psi]^*[/itex]

[itex]=[\int d^3x\bar\Psi\vec p\Psi]^*=<\vec p>^*=<\vec p>[/itex]

where [itex]<\vec p>[/itex] is real.

Is there anything wrong with my calculation, because my teacher didn't give me the grade for this?

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# Is <p>_c = -<p>?

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