Timeline for Spin 3/2 matrices in terms of Pauli matrices
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 28, 2016 at 10:44 | history | tweeted | twitter.com/StackPhysics/status/703893568319000576 | ||
| Feb 26, 2016 at 22:59 | answer | added | Cosmas Zachos | timeline score: 5 | |
| Feb 25, 2016 at 23:50 | comment | added | David Stephen | The reason I expect this to be possible is quite complicated.. it has to do vaguely with the fact that, when a spin 3/2 irrep is restricted to a subgroup $\mathbb{Z}_2 \times \mathbb{Z}_2$ inside SO(3), it must be isomorphic to two copies of the pauli representation. You are right about using CAS; I was just hoping for a quicker, more insightful route, especially since my skill with CAS is somewhat lacking. | |
| Feb 25, 2016 at 23:44 | comment | added | ACuriousMind♦ | Why would you expect a single unitary operator to do it for all three? And why do you not just write out the Kronecker product and look if the resulting system of linear equations has solutions or not (it's not a shame to use a CAS to solve systems of equations)? | |
| Feb 25, 2016 at 23:41 | history | edited | David Stephen | CC BY-SA 3.0 |
added 72 characters in body
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| Feb 25, 2016 at 23:40 | comment | added | David Stephen | Yes, it is clear for $\sigma_z$. But the unitary $U$ must be independent of $i$ so that it brings all three of the 3/2 matrices into the desired forms simultaneously. So $U=I$ would work for $\sigma_z$, but not the other two. Unless I am misunderstanding your comment, I don't see that this solves the problem. | |
| Feb 25, 2016 at 23:32 | comment | added | ACuriousMind♦ | Isn't it obvious that $\sigma_z(3/2) = \sigma_z(1/2)\otimes\mathrm{diag}(1,3)$, and since every $\sigma_i$ can be brought into $\sigma_z$'s form by a unitary transformations, that's it? | |
| Feb 25, 2016 at 23:21 | history | asked | David Stephen | CC BY-SA 3.0 |