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[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?