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theorems:cpt [2018/03/26 13:26]
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theorems:cpt [2018/05/05 12:23] (current)
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 <tabbox Intuitive> ​ <tabbox Intuitive> ​
 +The CPT theorem tells us that a mirror-image of our universe where we reverse all momenta (corresponding to the reversal of time) and with all matter replaced by anti-matter would evolve under exactly the same physical laws.
  
-<note tip> 
-Explanations in this section should contain no formulas, but instead, colloquial things like you would hear them during a coffee break or at a cocktail party. 
-</​note>​ 
-  ​ 
 <tabbox Concrete> ​ <tabbox Concrete> ​
 +The CPT theorem states that the product of charge conjugation,​ parity, and time rever-
 +sal transformations is under quite general assumptions a valid symmetry.
 +
 +The assumptions are:
 +
 +  * We are dealing with a quantum field theory.
 +  * It is based on a Hermitian, local, normal-ordered Lagrangian.
 +  * The Lagrangian is invariant under Lorentz transformations.
 +  * The canonical commutation or anti-commutation rules hold for the fields.
 +
 +Formulated differently,​ the CPT theorem says that any Lorentz invariant local [[theories:​quantum_field_theory:​canonical|quantum field theory]] with a Hermitian Hamiltonian must be CPT symmetric.
 +
 +From these assumptions it follows that the Lagrangian is also invariant under the produce of C, P, and T , taken in any order. Take note that $C$, $P$, $T$ or any other product of them can be violated, which CPT is intact. This means concretely that we can always choose the phases which appear in C, P, T transformations such that the product of those operators is a symmetry of our theory. ​
 +
 +In this sense, the combination CPT is more fundamental than the three
 +component transformations. ​
 +
 +To test the CPT symmetry we compare the masses, lifetimes, electric charges and anomalous magnetic
 +moments of particles with their corresponding antiparticles. Another possibility are detailed analysis of the behaviour of neutral flavoured meson systems.
 +
 +
 +
 +----
 +
 +  * For a nice discussion see Chapter 5 in “Discrete Symmetries and CP Violation: From Experiment to Theory” by Marco Sozzi
 +
  
-The CPT theorem says that any Lorentz invariant local [[theories:​quantum_theory:​quantum_field_theory|quantum field theory]] with a Hermitian Hamiltonian must be CPT symmetric. 
  
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theorems/cpt.1522063570.txt.gz · Last modified: 2018/03/26 11:26 (external edit)