- #1
qinglong.1397
- 108
- 1
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.
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?
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?