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nonequilibrium
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2 questions on symmetries: "conserved in interaction => eigenstate in interaction"?
Hello, I'm currently taking an introductory course in elementary particles (level: Griffiths) and I have 2 questions that are severely bothering me; all help is appreciated! They are related to Griffiths' "Introduction to Elementary Particles".
A) Say observable A (with operator [itex]\hat A[/itex]) is conserved in, say, the strong interaction, then why must any particle interacting with the strong force (incoming or outgoing) be in an eigenstate of [itex]\hat A[/itex]? For example in the strong interaction (which conserves S) particles must be in an S eigenstate, or in the presumption that the weak force conserves CP, the particles would have to be in a CP eigenstate to partake in weak decay. Why?
B) After establishing that the K-naught particles are not CP-eigenstates, Griffiths construes eigenstates [itex]| K_1 \rangle := \frac{1}{\sqrt{2}} \left( |K^0 \rangle - | \overline K^0 \rangle \right)[/itex] and analogously [itex]| K_2 \rangle[/itex] since if the weak force conserves CP, then kaons can only interact with the weak force in the forms of the (only) CP eigenstates [itex]|K_1 \rangle[/itex] and [itex]|K_2\rangle[/itex] (cf A). He then mentions that CP is not conserved, and finally claims (p147)
Hello, I'm currently taking an introductory course in elementary particles (level: Griffiths) and I have 2 questions that are severely bothering me; all help is appreciated! They are related to Griffiths' "Introduction to Elementary Particles".
A) Say observable A (with operator [itex]\hat A[/itex]) is conserved in, say, the strong interaction, then why must any particle interacting with the strong force (incoming or outgoing) be in an eigenstate of [itex]\hat A[/itex]? For example in the strong interaction (which conserves S) particles must be in an S eigenstate, or in the presumption that the weak force conserves CP, the particles would have to be in a CP eigenstate to partake in weak decay. Why?
B) After establishing that the K-naught particles are not CP-eigenstates, Griffiths construes eigenstates [itex]| K_1 \rangle := \frac{1}{\sqrt{2}} \left( |K^0 \rangle - | \overline K^0 \rangle \right)[/itex] and analogously [itex]| K_2 \rangle[/itex] since if the weak force conserves CP, then kaons can only interact with the weak force in the forms of the (only) CP eigenstates [itex]|K_1 \rangle[/itex] and [itex]|K_2\rangle[/itex] (cf A). He then mentions that CP is not conserved, and finally claims (p147)
But how does this follow? I have no clue! In Griffiths it was proven that K_1 and K_2 are CP eigenstates, so what is he saying?Evidently, the long-lived neutral kaon is not a perfect eigenstate of CP after all, but contains a small admixture of [itex]K_1[/itex]:
[itex]|K_L \rangle = \frac{1}{\sqrt{1+\epsilon^2}} \left( |K_2 \rangle + \epsilon |K_1 \rangle \right)[/itex]