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In weak desintegrations, the isospin is not necessarily conserved. But is the total angular momentum J=L+S+I always conserved?
Yes. The total angular momentum conservation is twin to energy and linear momentum conservation, and that has never been observed to be broken.quasar987 said:In weak desintegrations, the isospin is not necessarily conserved. But is the total angular momentum J=L+S+I always conserved?
quasar987 said:So the isospin is an angular momentum in the sense
He does !?quasar987 said:Cohen-Tanoudji defines angular momentum as any operator which satisfies the commutation relation [itex] [J_i,J_j]=\hbar\epsilon_{ijk}J_k[/itex].
So, what you are doing has no link with G-symmetry ? You were mentionning weak interaction. It maximally violates parity, so combining parity and isospin reverse, you often get (almost) conserved quatities...But it doesn't add to L and S.
The J=1/2 is wrong. Ispin has nothing to do with angular momentum.quasar987 said:This is not the answer I was hoping for!
I have this problem here that roughly says "a B particle disintegrate into a pi+ and a pi-". So I said "B has isospin 1/2, spin 0 and (there exists a ref. frame where B has) L=0. So that's J=1/2 for B. I know that the state ket for pipi must be symmetrical (2 indistinguishable bosons). And now I know that J total must be conserved.
Can someone show me the reasoning behind how to extract the nature (symmetric or antisymmetric) of [itex]|\pi^{+}\pi^{-}>[/itex] given the above information.
First sentence of p.646: This is why we shall adopt a more general view and define and angular momentum [itex]\mathbf{J}[/itex] as any set of three observables which satisfies: [itex] [J_i,J_j]=i\hbar\epsilon_{ijk}J_k[/itex]humanino said:He does !?
I don't know what G-symmetry is; this exercise is in the context of the Wigner-Eckart theorem in an ordinary undergrad QM class.humanino said:So, what you are doing has no link with G-symmetry ? You were mentionning weak interaction. It maximally violates parity, so combining parity and isospin reverse, you often get (almost) conserved quatities...
quasar987 said:First sentence of p.646: This is why we shall adopt a more general view and define and angular momentum ...
quasar987 said:First sentence of p.646: This is why we shall adopt a more general view and define and angular momentum [itex]\mathbf{J}[/itex] as any set of three observables which satisfies: [itex] [J_i,J_j]=i\hbar\epsilon_{ijk}J_k[/itex]
Isospin is a concept in particle physics that describes the symmetry between particles with different electric charges but the same strong interaction. It is important because it allows us to understand the behavior of particles in nuclear reactions and helps us classify and organize the different types of particles.
Conservation of angular momentum is a fundamental principle in physics that states that the total angular momentum of a system remains constant unless an external torque is applied. This principle also applies to isospin, as particles with different isospin values can interact and change their isospin states, but the total isospin of the system remains constant.
Isospin and spin are two distinct properties of particles, but they are related in that they both describe the intrinsic angular momentum of a particle. Isospin is specifically related to the strong interaction, while spin is related to the electromagnetic and weak interactions.
Isospin is crucial in the study of the strong nuclear force because it allows us to understand and predict the behavior of particles in nuclear reactions. By classifying particles based on their isospin values, we can determine how they will interact with each other through the strong force.
In nuclear reactions, isospin is conserved through the strong force. This means that the total isospin of the initial particles must equal the total isospin of the final particles. If this principle is violated, it indicates that another force, such as the weak or electromagnetic force, was involved in the reaction.