Weak Interaction Invariance Under CPT Symmetry

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Discussion Overview

The discussion centers around the invariance of weak interactions under CPT symmetry, exploring theoretical implications and the mathematical foundations of this concept within quantum field theories.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant asserts that weak interactions are CPT-invariant, referencing a theorem applicable to quantum field theories that meet certain conditions such as locality and unitarity.
  • Another participant requests further explanation on how to prove the invariance of weak interactions under CPT symmetry.
  • A later reply indicates that the proof of the CPT theorem is complex and requires substantial background knowledge, suggesting that it is a significant mathematical truth in quantum field theories.
  • Additionally, it is noted that experimental searches for CPT violation have not yielded results, and a potential violation would have profound implications for the understanding of fundamental symmetries in physics.

Areas of Agreement / Disagreement

Participants generally agree on the CPT invariance of weak interactions as a theoretical assertion, but there is no consensus on the ease of proving this invariance or the implications of potential CPT violation.

Contextual Notes

The discussion highlights the complexity of the CPT theorem and the necessity of specific mathematical frameworks for its proof, which may not be universally accessible to all participants.

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Is weak interaction invaraint under CPT Symmetry? Why?
 
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yes it is. it is a theorem that all quantum field theories that satisfy relatively weak conditions (locality, unitarity, S-matrix,...) are CPT-invariant. weak interactions are no exception. you can prove it by referring to that theorem, or by just brute-force transforming the action under CPT and seeing that it's invariant.
 
would you please expline further? How can I prove that?
 
Proof of the CPT theorem is nontrivial and requires quite a bit of background. But it is a deep and important mathematical truism about quantum field theories.

There are various books that treat it in varying degrees of rigor. I think Weinberg proves it in his volumes, and for a more mathematical treatment see Streeter/Wightman.

Incidentally people look for violation of the CPT experimentally, so far without success. But it would be a big deal if one day such a fundamental symmetry was broken. It would mean probably that we would need to go back to Constructive field theories for insight.
 

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