Derivative changes under CPT transformations

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Discussion Overview

The discussion centers on the behavior of derivatives under charge conjugation (C), parity (P), and time reversal (T) transformations, particularly in the context of vector fields such as the photon vector field. Participants explore how these transformations affect both the fields and their derivatives.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asks whether derivatives change sign under C, P, or T transformations, using the photon vector field as an example.
  • Another participant states that T changes coordinates as ##x^{\mu} \to -x^{\mu}##, while noting that charge does not affect spatial-temporal coordinates.
  • There is a claim that parity changes momentum but does not alter ##x^{\mu}##.
  • A participant expresses confusion about the effects of T and parity on the time component and spatial components of the coordinates.
  • A later reply confirms that under time reversal, ##\partial_0 \to -\partial_0##, while suggesting that the other derivatives remain unchanged.

Areas of Agreement / Disagreement

Participants express differing views on how T and parity affect the derivatives, indicating that the discussion remains unresolved with multiple competing interpretations.

Contextual Notes

There are uncertainties regarding the specific transformations of derivatives under different conditions, and participants have not reached a consensus on the effects of T and P on all components.

kelly0303
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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!
 
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##T## changes ##x^{\mu}\to -x^{\mu}## charge doesn't change spatial-temporal coordinates.
Parity changes momentum but doesn't change ##x^{\mu}##.
 
MathematicalPhysicist said:
##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?
 
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kelly0303 said:
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.
 

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