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--- theorems:cpt [2018/03/26 13:22]
jakobadmin
+++ theorems:cpt [2018/05/05 12:23] (current)
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 <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>
+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 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.
+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
+----
+<blockquote>A story has it that in the early sixties, Feynman was asked to give an evening
+talk to physics students at Caltech, explaining the basic idea of the CPT
+theorem: the celebrated result in quantum field theory that states that any
+relativistic (i.e. Lorentz-invariant) quantum field theory must be invariant
+under CPT, the composition of charge conjugation, parity reversal and time
+reversal. Feynman agreed to commit to doing this, commenting that if one cannot explain something to second year Caltech undergraduates then one
+does not understand it. The story goes that Feynman spent a month or two
+trying to plan the talk, and then, in despair, cancelled the commitment.<cite>[[https://pdfs.semanticscholar.org/3122/ede46d94feb43353ecea2a6416e15d296ccf.pdf|Towards a geometrical understanding of the CPT theorem]] by Hilary Greaves</cite></blockquote>
 <tabbox Abstract>
@@ Line 18: / Line 51: @@
 The CPT theorem tells us that CPT symmetry holds for all physical phenomena.
-<tabbox Research>
-  * For the experimental status of CPT symmetry see the [[https://arxiv.org/abs/0801.0287|Data Tables for Lorentz and CPT Violation]] by Alan Kostelecky, Neil Russell
 <tabbox FAQ>

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