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--- theorems:cpt [2018/03/29 13:37]
kennymann
+++ theorems:cpt [2018/04/16 17:49]
jakobadmin [Concrete]
@@ Line 5: / Line 5: @@
 <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|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_field_theory|quantum field theory]] with a Hermitian Hamiltonian must be CPT symmetric.
 ----

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