Timeline for Construction of interaction Lagrangian invariant under isospin $SU(2)$ transformations
Current License: CC BY-SA 3.0
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| Jan 17, 2017 at 21:38 | history | edited | Cosmas Zachos | CC BY-SA 3.0 |
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| Jan 17, 2017 at 19:45 | history | edited | Cosmas Zachos | CC BY-SA 3.0 |
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| Jan 17, 2017 at 13:55 | history | edited | Cosmas Zachos | CC BY-SA 3.0 |
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| Jan 15, 2017 at 14:34 | comment | added | Cosmas Zachos | Up to a point, you might. But, this change of basis is a rotation, the inverse isorotation of φ you saw worked out. | |
| Jan 15, 2017 at 11:04 | comment | added | Constantine Black | Can I say that the similarity transformation of $\tau _k $implies a change of basis in the space of the algebra since the algebra is isomorphic to the adjoint representation by definition of the last as a map to the algebra? So we change basis from the triplet of the φ to the basis of τ .Thank you. | |
| Jan 14, 2017 at 19:44 | vote | accept | Constantine Black | ||
| Jan 14, 2017 at 15:29 | history | edited | Cosmas Zachos | CC BY-SA 3.0 |
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| Jan 14, 2017 at 12:44 | comment | added | Cosmas Zachos | Two isospinors, each in its own 2d space, combine to a 3d isovector, $\psi^\dagger \tau^i \psi$, which is dotted to a fixed magnitude isovector $\phi^i$ to yield the isosinglet. All isorotations are in the internal isospin space, but are formally identical to space rotations. You learn about the rotation group in basic Quantum Mechanics books, where you must do all angular momentum exercises to understand basic group representation theory. | |
| Jan 14, 2017 at 10:45 | comment | added | Constantine Black | Also, can we say that the transformation of $\phi \cdot t $ is a rotation of a vector by showing that the absolute value of $\phi $ remains the same; but in what vector space does this rotation takes place? Why does that rotation gives us the transformation of the adjoint vector in the fundamental representation( or have I misunderstood)? And just for being more precise: how and what are now the term in both representation spaces that are now invariant; or do we have the invariants now in another space? Again, thank you and if there are any references from where I could study please inform me. | |
| Jan 14, 2017 at 10:39 | comment | added | Constantine Black | Thank you Professor, I appreciate your response and help. Minor questions: you write 2x2x3 and not 2x3 for the direct product of representations; is that because we have two iso-fermions in the scattering or because you are using both $\psi$ and $\psi$ dagger? | |
| Jan 13, 2017 at 23:17 | history | edited | Cosmas Zachos | CC BY-SA 3.0 |
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| Jan 13, 2017 at 22:39 | history | edited | Cosmas Zachos | CC BY-SA 3.0 |
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| Jan 13, 2017 at 22:30 | history | edited | Cosmas Zachos | CC BY-SA 3.0 |
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| Jan 13, 2017 at 20:50 | history | answered | Cosmas Zachos | CC BY-SA 3.0 |