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quasar987

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quasar987

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Yes. The total angular momentum conservation is twin to energy and linear momentum conservation, and that has never been observed to be broken.

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quasar987

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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.

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Usually, J=S+L is the total angular momentum. Isospin is analogous to spin but acts in internal space, unlike spin and angular momentum.

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quasar987

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Tom Mattson

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No, isospin isn't angular momentum inSo the isospin is an angular momentum in the sense

I think you're getting 2 different things confused here. You quote the total angular momentum as J=L+S+I, and then call I the isospin. But most textbooks refer to I as the

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quasar987

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This is why I called the isospin an angular momentum.

But it doesn't add to L and S.

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He does !?Cohen-Tanoudjidefinesangular momentum as any operator wich satisfies the commutation relation [itex] [J_i,J_j]=\hbar\epsilon_{ijk}J_k[/itex].

That only defines a symmetry group, not to what the symmetry is applied (as Tom Mattson said).

I am quite bugged.

So, what you are doing has no link with G-symmetry ? You were mentionning weak interaction. It maximally violates parity, so combining parityBut it doesn't add to L and S.

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Meir Achuz

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The J=1/2 is wrong. Ispin has nothing to do with angular momentum.

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.

Just the math is similar.

The two pions have L=0, a symmetrical state.

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quasar987

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First sentence of p.646: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.So, what you are doing has no link with G-symmetry ? You were mentionning weak interaction. It maximally violates parity, so combining parityandisospin reverse, you often get (almost) conserved quatities...

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First sentence of p.646:This is whywe shall adopt a more general view and define and angular momentum ...

what is the previous sentence... or what was he talking about

As Meir Achuz said, the pions are in a L=0 state, which must be symmetrical.

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quasar987

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Tom Mattson

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OK, fine: IsospinFirst 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]

[tex][\tau_i,\tau_j]=i\epsilon_{ijk}\tau_k[/tex]

There are no angular momentum units anywhere in there.

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Tom Mattson

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Actually, I've been thinking about my last post and I'm not satisfied with it. In natural units (where [itex]\hbar=1[/itex]), the algebras **are** identical. So that's not why isospin is not an angular momentum.

Angular momentum is the generator of rotations in the normal 3-space in which we all live. It is conserved in physical systems that are invariant under rotations*in ***that** space. Isospin, on the other hand, is the generator of rotations in a completely different space altogether, called isospin space. Isospinors are not elements of the eigenspace of [itex]J[/itex], and neither are spinors elements of isospin space. And there is no reason that conservation of [itex]J[/itex] should imply anything about conservation of [itex]\tau[/itex], and vice versa.

Angular momentum is the generator of rotations in the normal 3-space in which we all live. It is conserved in physical systems that are invariant under rotations

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