- #1
LayMuon
- 149
- 1
We know that under charge conjugation the current operator reverses the sign:
[tex]
\hat{C} \hat{\bar{\Psi}} \gamma^{\mu} \hat{\Psi} \hat{C} = - \hat{\bar{\Psi}} \gamma^\mu \hat{\Psi}
[/tex]
Here [itex] \hat{C} [/itex] is the unitary charge conjugation operator. I was wondering should we consider gamma matrix here as also an entity undergoing transformation (like when we prove form-covariance of Dirac equation under any unitary transformation): [itex] \hat{C} \gamma^{\mu} \hat{C} = \gamma^{\prime \mu} [/itex]? Or gamma matrix is something of a structure ensuring element and should not be changed?
[tex]
\hat{C} \hat{\bar{\Psi}} \gamma^{\mu} \hat{\Psi} \hat{C} = - \hat{\bar{\Psi}} \gamma^\mu \hat{\Psi}
[/tex]
Here [itex] \hat{C} [/itex] is the unitary charge conjugation operator. I was wondering should we consider gamma matrix here as also an entity undergoing transformation (like when we prove form-covariance of Dirac equation under any unitary transformation): [itex] \hat{C} \gamma^{\mu} \hat{C} = \gamma^{\prime \mu} [/itex]? Or gamma matrix is something of a structure ensuring element and should not be changed?