Derivative changes under CPT transformations

[kelly0303]

Hello! Do the derivatives change sign under C, P or T transformation. For example, for the photon vector field we have, under C, $A_\mu \to -A_\mu$. Do we also get $\partial_\mu \to -\partial_\mu$? And what about P and T? Thank you!

 

[MathematicalPhysicist]

$T$ changes $x^{\mu}\to -x^{\mu}$ charge doesn't change spatial-temporal coordinates.
Parity changes momentum but doesn't change $x^{\mu}$.

 

[kelly0303]

$T$ changes $x^{\mu}\to -x^{\mu}$ charge doesn't change spatial-temporal coordinates.
Parity changes momentum but doesn't change $x^{\mu}$.

I am a bit confused. Shouldn't we have that T changes $x^0 \to -x^0$ and Parity would do the same for the other 3 components?

 

[MathematicalPhysicist]

I am a bit confused. Shouldn't we have that T changes $x^0 \to -x^0$ and Parity would do the same for the other 3 components?

yes.
So $\partial_0 \to -\partial_0$ under time reversal while the other derivatives stay the same.