CPT Invariance of Hermitian & Lorentz Lagrangians

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SUMMARY

All Hermitian and Lorentz invariant Lagrangians are indeed invariant under the combination of CPT (Charge, Parity, Time reversal) symmetry. The discussion references a rigorous proof of the CPT theorem, which establishes that Lorentz invariance is not a prerequisite for CPT symmetry. Furthermore, the violation of CPT does not imply a violation of Lorentz invariance, highlighting the independence of these two fundamental symmetries in theoretical physics.

PREREQUISITES
  • Understanding of Hermitian operators in quantum mechanics
  • Familiarity with Lorentz invariance in relativistic physics
  • Knowledge of CPT symmetry and its implications
  • Basic grasp of Lagrangian mechanics
NEXT STEPS
  • Study the rigorous proof of the CPT theorem as outlined in the provided paper
  • Explore the implications of Lorentz invariance in quantum field theory
  • Investigate examples of Lagrangians that exhibit CPT symmetry
  • Examine cases of CPT violation and their consequences in particle physics
USEFUL FOR

The discussion is beneficial for theoretical physicists, quantum mechanics researchers, and students studying advanced topics in particle physics and field theory.

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Are all the hermitian and lorentz invariant lagrangians, invariant under the combination of CPT?

If yes, how can it be proved?
 
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http://users.ox.ac.uk/~mert2255/papers/cpt.pdf

Here is a rigorous proof of the CPT-theorem...
In a general framework, Lorentz invariance is not needed for CPT symmetry to exist. Neither the violation of CPT would necessarily mean the violation of Lorentz invariance.
 

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