theorems:cpt
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theorems:cpt [2018/03/26 13:28] jakobadmin [Intuitive] |
theorems:cpt [2018/05/05 12:23] (current) jakobadmin ↷ Links adapted because of a move operation |
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| 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. | 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. | ||
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| <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. | ||
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| + | The assumptions are: | ||
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| + | * 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. | ||
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| + | 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. | ||
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| + | 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. | ||
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| + | In this sense, the combination CPT is more fundamental than the three | ||
| + | component transformations. | ||
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| + | 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. | ||
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| + | ---- | ||
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| + | * For a nice discussion see Chapter 5 in “Discrete Symmetries and CP Violation: From Experiment to Theory” by Marco Sozzi | ||
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| - | 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.1522063680.txt.gz · Last modified: 2018/03/26 11:28 (external edit)
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