Weak Interaction Invariance Under CPT Symmetry

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SUMMARY

Weak interactions are invariant under CPT symmetry, as established by the CPT theorem applicable to all quantum field theories that meet specific conditions such as locality and unitarity. This theorem can be demonstrated either through reference to its proof or by transforming the action under CPT to show invariance. Notable references for understanding this theorem include Steven Weinberg's volumes and the mathematical treatment by Streater and Wightman. Despite ongoing experimental searches for CPT violation, no evidence has been found, which would necessitate a reevaluation of fundamental theories if discovered.

PREREQUISITES
  • Understanding of quantum field theory principles
  • Familiarity with the concepts of locality and unitarity
  • Knowledge of the S-matrix formalism
  • Basic mathematical background in theoretical physics
NEXT STEPS
  • Study the CPT theorem in depth through Steven Weinberg's "The Quantum Theory of Fields"
  • Explore the mathematical framework in "Quantum Field Theory and Statistical Mechanics" by Streater and Wightman
  • Investigate experimental methods for detecting CPT violation
  • Research Constructive field theories for insights into fundamental symmetries
USEFUL FOR

The discussion is beneficial for theoretical physicists, quantum field theorists, and researchers interested in the implications of fundamental symmetries in particle physics.

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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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